Receiver device and communication system

ABSTRACT

A communication system that sends and receives signals via each of two adjacent channels ch 1  and ch 2  in which interchannel interference exists, wherein the receiver device comprises a soft decision target value generation unit for each of a plurality of received bits inputted from the corresponding channel; and a soft decision unit that makes a soft decision with respect to each of the plurality of received bits by using the respective soft decision target values. Each soft decision target value generation unit generates its own soft decision target values by using the respective soft decision target values of the plurality of bits inputted from the receiver device of the other channel and the soft decision unit makes a decision with respect to the received bits on the basis of the soft decision target values.

BACKGROUND OF THE INVENTION

The present invention relates to a receiver device and communicationsystem and, more particularly, to a receiver device and communicationsystem that utilize interchannel interference in a communication systemthat comprises two or more channels or subchannels, that is, asingle-carrier communication system comprising two orthogonal channels,a multicarrier communication system with filterbank modulation, DMT(Discrete Multi-Tone) modulation, FMT (Filtered Multi-Tone) modulation,or the like, or an OFDM or OFDM-CDMA multicarrier modulationcommunication system in which bandwidth is divided into a multiplicityof independent narrow subbands each of which is independently modulated.Further, when ‘channel’ appears hereinafter, same is intended to includesuch subchannels.

The bit error rate (BER) of a single carrier communication systemcomprising two orthogonal channels, or a multicarrier communicationsystem or multicarrier modulation communication system permitsadditional improvement by utilizing a received signal that includesdistortion arising from Inter Channel Interference (ICI). Inter ChannelInterference is produced as a result of an unavoidable environmentsubject to orthogonal loss between channels that arises due to a systemmalfunction of the communication system or a time-varying channel. TheInter Channel Interference arises from the leakage of spectral energy orwhat is known as ‘interchannel crosstalk’.

The main advantage of the turbo receiver of the present invention isthat the behavior of the ICI is treated as a probability variable of aGaussian distribution with a zero mean value (a Gaussian approximationthat is used in D. Froney. Jr, and M. V. Eyuboglu, “CombinedEqualization and Coding Using Precoding”, IEEE Commun. Magazine, pp.25-34, Dec. 1991, for example) and for which a finite-state discreteMarkov process model is adopted. With this ICI model, a simple Gaussianapproximation may be considered to be more realistic from theperspective the ICI quality. The turbo receiver of the present inventionis based on a maximum posterior probability estimation algorithm. Thisturbo receiver is such that information that is derived from a firstchannel following nonlinear processing is used to examine the estimatedmaximum posterior probability and, similarly, information that isderived from the second channel is used to examine the estimated maximumprobability of the first channel.

(a) Multicarrier Communication System

In a multicarrier communication system with filterbank modulation, DMT(Discrete Multi-Tone) modulation, FMT (Filtered Multi-Tone) modulation,or the like, that is, a multicarrier communication system that dividesbandwidth into a plurality of subbands that are independent bandwidthsand performs modulation according to transmission data for each subbandindependently, the selection of the filter set has traditionally beenexecuted with the constraint that the Inter Symbol Interference (ISI)and Inter Channel Interference (ICI) be completely removed.

In the case of a virtual transmission channel with which there is noDoppler shift and no frequency offset between transmitter and receiver,that is, which does not induce signal distortion, this constraintguarantees error-free recovery of a transmission symbol by the receiver.However, a frequency offset that is produced in each channel as a resultof inaccurate tuning of the oscillator or due to a Doppler shift bringsabout BER distortion due to spectral leakage or ICI.

The sole method of alleviating such BER deterioration is that of makingthe frequency offset as small as possible, more specifically, keepingsame within 1% of the subcarrier frequency interval. However, thismethod necessitates an exact frequency offset estimation and there isthe problem that, when a multicarrier signal mixed with noise isreceived and the noise level is large, the accuracy of the frequencyoffset estimation is impaired. In addition, this method does not workproperly in the case of a high-speed phasing channel, that is, in thecase of a high-speed phasing channel for which the Doppler shift isfixed with respect to the transmission symbol and varies with time.

As shown in FIG. 1, if the frequency offset (the frequency offsetnormalized according to the channel interval) a is zero (a=0), thetransmission function of the first subchannel (gain/frequencycharacteristic) produces infinite decay at the center frequency f₂ ofthe second subchannel (dotted line), as shown by the solid line inFIG. 1. Further, the transmission function of the second subchannellikewise produces infinite decay at the center frequency f₁ of the firstsubchannel. That is, if the frequency offset a is zero, ICI is notproduced between adjacent subchannels. In other words, if the frequencyoffset a is zero, the subchannels are orthogonal and the ICI does notexist at all. FIG. 2 shows the subchannel characteristic when thefrequency offset a (≠0) exists in a DMT system. If the frequency offseta is not zero, each spectrum of the adjacent subchannel exhibits anon-zero reciprocal gain at the subchannel frequencies f₁ and f₂ ofinterest, which are specified as a₂₁ and a₁₂ in FIG. 2. That is, asshown in FIG. 2, when the frequency offset is not zero, ICI (crosstalk)is produced between subchannels.

(b) Single Carrier Communication System

With single-carrier modulation methods that are extensively used atpresent, the receiver must incorporate a Quadrature down converter(quadrature decoder). This must subject the RF signal or localoscillator output to a 90° phase shift. The phase shift of the RF signalis generally accompanied by a trade-off with a noise output gain and thephase shift of the RF signal is problematic in the case of a wide bandsignal of a high-speed data system. Hence, the phases of the I and Qsignals (see FIG. 3) are desirably shifted. So too when there is anerror in the 90° phase shift or mismatch of the Q quadrature signalamplitudes, the constellation of the signal that has been frequencydown-converted (quadrature-decoded signal) is degraded, whereby the BERis increased. FIG. 3 represents an ideal case where the I and Q signalamplitudes are equal and the phases of the I and Q signals areorthogonal and FIG. 4 represents a case (phase error case) where the Iand Q signal amplitudes are not equal or the phases of the I and Qsignals are not orthogonal. In FIG. 4, because the phases of the I and Qsignals (I′, Q′) are not orthogonal or the amplitudes thereof are notequal, an ICI Quadrature component is produced as indicated by the boldlines Iq and Qi.

The action of keeping the phase shift offset at 4 to 7° in order toretain the same quality as when there is no phase offset and the phaseshift between the RF signals or I, Q signals is 90° was establishedthrough experimentation. As detailed earlier, conventional communicationsystems are faced by the problem that ICI occurs due to a frequencyoffset, phase error, or amplitude error, or the like, and the BERdegrades as a result of this ICI.

(c) A General System Model

FIG. 5 is a multicarrier system in which the frequency offset shown inFIG. 2 exists or is a model of 2-channel ICI in a single-carrier systemin which the orthogonal mismatch shown in FIG. 4 exists. 1 and 2 aretransmitter devices of first and second subchannels ch.1 and ch.2respectively; 3 and 4 are receiver devices of subchannels ch.1 and ch.2respectively; 5 and 6 are the transmission channels of each subchannel;7 and 8 are multipliers that multiply, for each of channel signalsS_(1l)*(t), S_(2l)*(t), the crosstalk coefficients α₁₂, α₂₁; 9 and 10are synthesizers that synthesize the crosstalk (ICI) from the othersubchannels with the channel signal of the respective synthesizers' ownchannel; and 11 and 12 are noise synthesizers. As can be seen from FIG.5, the first subchannel signal leaks to the second subchannel accordingto the coupling coefficient α₁₂ and the second subchannel signal leaksto the first subchannel according to the coupling coefficient α₂₁. As aresult of the intersubchannel frequency orthogonal, the noisecomponents, which are expressed as n₁(t) and n₂(t) are statisticallyindependent (no correlation).

Assuming a case where binary information is transmitted via the firstand second subchannels by means of multiple value modulation method 16QAM with a symbol cycle T, each point of the 16 QAM constellation inFIG. 6 is expressed by a 4-bit symbol made up of common mode componentsi₁, i₂, and quadrature components q₁, q₂. Further, the four bits areinterleaved for the sequence i₁q₁i₂q₂. The Quadrature components I and Qare each graycoded through allocation of the bits 01, 00, 10, and 11,which correspond to the levels 3d, d, −d, and −3d respectively.

The model in FIG. 5 is advantageous from the point of view ofunderstanding the physical process that is the cause of ICI. If thismodel is used, the task is to be able to determine accurately the valuesof the received signals, the transmission information symbols, and soforth of each subchannel even when ICI is produced.

One possible method of alleviating ICI in a receiver device adopts thedecision feedback equalizer (DFE) for ICI cancellation that is proposedby G. Cherubini, E. Eiefheriou, S. Olcer, and J. M. Cioffi, “Filter bankmodulation techniques for very high speed digital subscriber line”, IEEECommun. Magazine, vol. 38, pp. 98-104, May 2000.

Further, when the individual receiver device outputs are subject to ahard bit decision (hard decision) mode, there is barely any advantage insharing information between the subchannels. The soft decision restrictsthe operational scope of the DFE according to the high SN ratio.

Even when the above approach is effective in a great number of realcases, minimizing the effects of ICI is essentially a quasi-optimumvalue. This is because, information on the transmission symbol iscontained in the interference wave. The reliability of data transmissioncan be raised by means of optimal reception of a signal that is based onmaximum posterior probability estimation.

An OFDM receiver that corrects errors in the phases and frequency ofdigital multiple carrier wave signals has been proposed as a firstconventional technology (JP11-154926A). With this first conventionaltechnology, in addition to demodulation FFT processing, the OFDMreceiver performs FFT processing to evaluate its own noise component andprevents crosstalk (ICI) by performing correction processing so that theorthogonal remains between the carrier waves prior to the demodulationFFT processing on the basis of the evaluated own noise component.

Further, an OFDM receiver device that removes an intercarrierinterference component that exists in the Fourier Transform output hasbeen proposed as a second conventional technology (JP 2001-308820A).According to this second conventional technology, a filter coefficientis sequentially calculated by means of an adaptive algorithm to removethe carrier interference component from a frequency domain signal thatconstitutes the Fourier Transform output of the OFDM receiver and isestablished for an adaptive filter that is provided on theFourier-Transform output side.

Moreover, the present inventors have proposed a receiver device thatreceives on each of two adjacent channels and closely examines theestimated probability of information on the second channel by means ofthe estimated probability of information on the first channel and,similarly, closely examines the estimated probability of information onthe first channel by means of the estimated probability of informationon the second channel (see WO 2004/023684). In this receiver device, thereceiver portion that is provided on each channel calculates thedifference between the probability that data received from thecorresponding channel will be “0” and the probability that the data willbe “1” as a soft decision target value in consideration of the degree ofcoupling between channels and adjusts and outputs its own soft decisiontarget value by using the soft decision target value of the secondchannel that is inputted from the other receiver portion, whereby the“0” and “1” of the received data is judged on the basis of the adjustedsoft decision target value.

However, the first and second conventional technologies do notdemodulate the received signal so that the BER performance improves byusing transmission symbol information that is contained in the ICIsignal from the second channel.

Although the principle of the receiver device of the third conventiontechnology is useful, the corresponding one bit of the adjacentsubchannel is demodulated by using ICI but a plurality of bits are notdemodulated by using ICI as one unit. For this reason, in communicationsin which a plurality of bits are taken as a single unit as permulti-value QAM modulation, there is the problem that reception anddemodulation that uses information of a plurality of bits of the secondchannel is impossible.

SUMMARY OF THE INVENTION

An object of the present invention is to propose an optimal receptionmethod and receiver device for a multi-value QAM signal that are basedon maximum posterior probability estimation and to raise the reliabilityof multi-value QAM data transmission.

A further object of the present invention is to enhance the BERperformance of the receiver device by using information of a pluralityof bits of the second channel to demodulate a plurality of bits of itsown channel.

A further object of the present invention is to reduce BER by usinginformation of a plurality of bits of the multi-value QAM modulation ofthe second channel to demodulate multi-value QAM modulation data of itsown channel.

The above objects are achieved by implementing a turbo algorithm andnonlinear signal processing. Hence, according to the present invention,after nonlinear processing, information of a plurality of bits that isderived from the first channel is used to examine closely the estimatedposterior probability (soft decision target value) of the secondchannel-and, likewise, after nonlinear processing, information of aplurality of bits that is derived from the second channel is used toexamine closely the estimated posterior probability (soft decisiontarget value) of the first channel.

The present invention is a single-carrier or multicarrier communicationsystem having two channels that comprises two multi-value QAM modulationtransmitter devices that transmit data independently via each channel, afirst crosstalk path with a coefficient a₁₂ for coupling from the firstchannel to the second channel, a second crosstalk path with a couplingcoefficient a₂₁ for coupling from the second channel to the firstchannel, and two receivers for each channel. Preferably, the receiversof the in-phase component I and the Quadrature component Q are analogousand each comprise two parts, wherein the first part receives a firstnumber-one bit and the second part receives a second number-two bit.

The communication system of the present invention comprises twotransmitter devices that transmit data of one unit independently in aplurality of bits via two adjacent channels; two receiver devicesprovided in each channel that generates a soft decision target value foreach of a plurality of received bits of one unit inputted from thecorresponding channel and makes a soft decision with respect to theplurality of received bits by using the respective soft decision targetvalues; and means for inputting the soft decision target values of theplurality of received bits of the first receiver device of one channelto the second receiver device of the other channel, wherein the secondreceiver device adjusts its own soft decision target values by using therespective soft decision target values inputted by the first receiverand makes a decision with respect to the received bits on the basis ofthe soft decision target values.

In a case where data of one unit is two-bit data of an in-phasecomponent or a quadrature component that has been obtained bymulti-value QAM modulation, the first channel/first bit receiver portionof the receiver device comprises (1) two first and second correlationmeans that integrate the multiplication results obtained by multiplyingan input signal by predetermined reference signals; (2) three first tothird nonlinear units having a transmission function of an amplitudelimiter comprising a linear region; (3) a multiplication unit thatmultiplies the outputs of the nonlinear units by weighting functions;(4) a synthesizer that generates a soft decision target value of thefirst bit of the first channel by synthesizing each weightedmultiplication unit output and the output of the first correlationmeans; (5) an adder circuit that adds the soft decision target values ofthe first and second bits of the second channel to the output signalsfrom the first and second correlation means respectively and then inputsthe addition results to the first and second nonlinear unitsrespectively; and (6) an adder circuit that adds the soft decisiontarget value of the second bit of the first channel to the output signalfrom the second-correlation means and inputs the addition result to thethird nonlinear unit.

Further, in cases where data of one unit is two-bit data of an in-phasecomponent or quadrature component that has been obtained by multi-valueQAM modulation, the first channel/second bit receiver portion of thereceiver device of the present invention comprises (1) three first,second and third correlation means that integrate the multiplicationresults obtained by multiplying an input signal by predeterminedreference signals; (2) three first to third nonlinear units having atransmission function of an amplitude limiter comprising a linearregion; (3) an adder circuit that adds the soft decision target valuesof the second and first bits of the second channel respectively to theoutput signals from the second and third correlation means and theninputs the addition results to the first and second nonlinear unitsrespectively; (4) a calculation unit that multiplies the output signalfrom the first correlation means by a predetermined value and then addsthe multiplication result to the outputs of the first and secondnonlinear units; (5) an adder circuit that adds the soft decision targetvalue of the first bit of the first channel to the output of thecalculation unit and then inputs the addition result to the thirdnonlinear unit, wherein the soft decision target value of the second bitof the first channel is produced on the basis of the output of the thirdnonlinear unit.

The present invention proposes an optimal reception method and receiverdevice for a multi-value QAM signal based on maximum posteriorprobability estimation, whereby the reliability of the multi-value QAMdata transmission can be increased.

Further, according to the present invention, the BER performance of thereceiver device can be enhanced by using information of a plurality ofbits of the second channel to demodulate a plurality of bits of its ownchannel.

In addition, according to the present invention, the BER can be reducedby using information of a plurality of bits of the multi-value QAMmodulation of the second channel to demodulate the multi-value QAMmodulation data of its own channel.

Other features and advantages of the present invention will be apparentfrom the following description taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a frequency characteristic when the frequency offset a iszero;

FIG. 2 is a frequency characteristic when the frequency offset a iszero;

FIG. 3 is an explanatory diagram of a signal vector (constellation) inan ideal case where the signal amplitudes of demodulated signals I and Qare equal and the phases of signals I and Q are orthogonal;

FIG. 4 is an explanatory diagram of a signal vector (constellation) in acase where the amplitudes of signals I and Q are not equal or the phasesof signals I and Q are not orthogonal;

FIG. 5 is a general model serving to illustrate a multicarriercommunication system or single-carrier communication system in which ICIexists;

FIG. 6 is an explanatory diagram of a 16 QAM constellation;

FIG. 7 shows the overall constitution of the communication system of thepresent invention that decodes received data by using interferencebetween two adjacent channels;

FIG. 8 is a transmission function for a nonlinear unit;

FIG. 9 is a synthesized transmission function when nonlinear units aresynthesized;

FIG. 10 is a constitutional view of the first channel/first bit receiverportion the present invention;

FIG. 11 is a transmission function for a nonlinear unit FΣ(x, ΔE₁, ΔE₂);

FIG. 12 is a constitutional view of the first channel/second bitreceiver portion of the present invention;

FIG. 13 is a constitutional view of the receivers of the first andsecond channels;

FIG. 14 is an explanatory diagram of constellations of the first channelwith different points of the communication system shown in FIG. 7;

FIG. 15 shows the results of a simulation in which the average BERperformance of the first bit i₁ of the receiver of the present inventionis shown as the function 2Eb/No; and

FIG. 16 shows the results of a simulation in which the average BERperformance of the first bit i₂ of the receiver of the present inventionis shown as the function 2Eb/No.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is a communication system that sends and receivessignals via two adjacent channels in which interchannel interferenceexists, wherein the receiver device comprises a soft decision targetvalue generation unit that generates soft decision target values foreach of a plurality of received bits inputted from the correspondingchannel; and a soft decision unit that makes a soft decision withrespect to each of the plurality of received bits by using therespective soft decision target values. Each soft decision target valuegeneration unit generates its own soft decision target value by usingeach soft decision target value of the plurality of bits inputted by thereceiver device of the other channel and the soft decision unit judgesthe received bits on the basis of the soft decision target values.

(A) The Overall Constitution of the Communication System of the PresentInvention

FIG. 7 shows the overall constitution of the communication system of thepresent invention that decodes received data by using interferencebetween two adjacent subchannels. The communication system comprises twotransmitter units 21 and 22, which transmit data independently viaadjacent subchannels ch1 and ch2, two receiver units 30 and 40, whichare provided in each subchannel, receive data from the correspondingsubchannel, and make a soft decision with respect to the received data,and means 50 for inputting the soft decision target values of eachreceiver unit to the other receiver unit. The receiver units 30 and 40comprise receiver portions 31 and 41 respectively and first and seconddecision units 32, 33 and 42, 43 respectively.

The first receiver unit 30 (40) uses the soft decision target value thatis inputted by the second receiver unit 40 (30) to adjust its own softdecision target value and judges whether the code of the received datais “+” or “−”, that is, “0” or “1” on the basis of the soft decisiontarget value. Further, as transmission path characteristics, a firstcrosstalk path 51, which has a coefficient a₁₂ for coupling from thefirst subchannel ch1 to the second subchannel ch2 and a second crosstalkpath, which has the coefficient a₂₁ for coupling from the secondsubchannel ch2 to the first subchannel ch1 exist, these first and secondsubchannels being expressed by the numerals 51 and 52 respectively.Further, the ICI signal and noise are synthesized during transmissionand the parts performing this synthesis are expressed by the numerals53, 55 and 54, 56 respectively.

(B) Reception Symbol Demodulation Algorithm

The receiver units of the first and second subchannels of thecommunication system shown in FIG. 7 will now be described with respectto the algorithm for demodulating the reception symbols.

Assuming a case where binary information is transmitted by thetransmitter units 21 and 22 via the first and second channels by meansof a symbol cycle T and the multi-value modulation method 16 QAM, in the16 QAM constellation of FIG. 6, each point is expressed by a 4-bitsymbol made up of common mode components i₁ and i₂ and Quadraturecomponents q, and q₂. Further, the four bits are interleaved for thesequence i₁q₁i₂q₂. The Quadrature components I and Q are graycodedthrough allocation of the bits 01, 00, 10, and 11, which correspond tothe levels 3d, d, −d, and −3d.

According to the mapping in FIG. 6, the Hamming distance between twoadjacent constellation points that exist closest to a Euclidean distanceof 2d is always one. This is the basic characteristic of the gray codeprocess whereby, even when the quality of transmitted data deterioratessuch that erroneous identification of adjacent constellation pointsoccurs due to noise, the decoder only produces a single bit error. Thisminimizes the probability of total bit error. As detailed earlier, theorthogonal coordinates I and Q can be defined by Table 1 below: TABLE 1Signal Signal Signal No i₁ i₂ Signal in I No q₁ q₂ in Q S₀*(t) 0 1 +3dS₀*(t) 0 1 +3d S₁*(t) 0 0  +d S₁*(t) 0 0  +d S₂*(t) 1 0  −d S₂*(t) 1 0 −d S₃*(t) 1 1 −3d S₃*(t) 1 1 −3d

Because bits i₁q₁i₂q₂ in 4-bit 16 QAM are statistically independent, theorthogonal signals (see Table 1) are also independent. Further, I and Qare orthogonal and, hence, there is generally no loss of any kind andthe analysis can be restricted to an analysis of only one orthogonalsignal such as only an in-phase component I, for example. In this case,all the results obtained for component I can also be applied tocomponent Q.

Here, the channel signal of the output of the 16 QAM modulator isS_(il)*(t). Using this notation, the initial index i denotes the channelnumber (1 or 2) and the second index denotes l={0,1,2,3}. According toTable 1, l=0, l=1, l=2, l=3 signifies i₁i₂=“01”, i₁i₂=“00”, i₁i₂=“10”,and i₁i₂=“11” respectively. That is, l is determined by the two bits i₁,i₂ of the common mode component I. Henceforth, in order to simplify thenotation, the notation becomes s_(il)*(t)→S_(il)*; in order to omit thetime dependency of signal S_(il)*(t). Signals affected by ICI at theinputs of the receiver units of the first and second channels from FIG.7 can be expressed according to the following equation based on thelinear coupling of the transmission signals S_(1l)*, S_(2l)* of thefirst and second channels, where α₁₂=α₂₁=α.S _(1j) =S _(1l) *+α·S _(2l) *, S _(2j) =S _(2l) *+α·S _(1l)*;l={0,1,2,3}, j={0,1, . . . ,15}  (1)

Only the first channel is considered here. The results for the secondchannel are obtained in the same manner. Table 2 shows the relationshipbetween the received signal of the first channel and the transmissionsignals of the first and second channels in a case where S_(1j)=Sj.TABLE 2 Channel 1 Channel 2 Signal in Chan. 1 S_(1l)* i₁ i₂ S_(2l)* i₁i₂ S₀ = S₁₃* + α · S₂₃* −3d 1 1 −3d 1 1 S₁ = S₁₃* + α · S₂₂* −3d 1 1  −d1 0 S₂ = S₁₃* + α · S₂₀* −3d 1 1  +d 0 1 S₃ = S₁₃* + α · S₂₁* −3d 1 1+3d 0 0 S₄ = S₁₂* + α · S₂₃*  −d 1 0 −3d 1 1 S₅ = S₁₂* + α · S₂₂*  −d 10  −d 1 0 S₆ = S₁₂* + α · S₂₀*  −d 1 0  +d 0 1 S₇ = S₁₂* + α · S₂₁*  −d1 0 +3d 0 0 S₈ = S₁₀* + α · S₂₃* +3d 0 1 −3d 1 1 S₉ = S₁₀* + α · S₂₂*+3d 0 1  −d 1 0 S₁₀ = S₁₀* + α · S₂₀* +3d 0 1  +d 0 1 S₁₁ = S₁₀* + α ·S₂₁* +3d 0 1 +3d 0 0 S₁₂ = S₁₁* + α · S₂₃*  +d 0 0 −3d 1 1 S₁₃ = S₁₁* +α · S₂₂*  +d 0 0  −d 1 0 S₁₄ = S₁₁* + α · S₂₀*  +d 0 0  +d 0 1 S₁₅ =S₁₁* + α · S₂₁*  +d 0 0 +3d 0 0

According to Equation (1), after ICI has been considered, the input ofthe receiver unit of each channel has sixteen signals for j={0, 1, 2, .. . , 15} rather than the four transmission signals l={0, 1, 2, 3}.

The posterior probability of receiving the signal S_(j) on the ithchannel from Table 2 is given by the following equation according toBayes' mixed rule: $\begin{matrix}\begin{matrix}{{P_{i}\left\lbrack {i_{1},{i_{2}/{y(t)}}} \right\rbrack} = {P_{i}\left\lbrack {S_{j}/{y(t)}} \right\rbrack}} \\{= \frac{{P_{apr}\left( S_{j} \right)} \cdot {P\left( {{y(t)}/S_{j}} \right)}}{P\left( {y(t)} \right)}} \\{\equiv {{k_{0} \cdot {P_{apr}\left( S_{j} \right)} \cdot \exp}\left\{ {{- \frac{1}{N_{0}}}{\int_{0}^{T}{\left\lbrack {{y(t)} - S_{j}} \right\rbrack^{2}\quad{\mathbb{d}t}}}} \right\}}}\end{matrix} & (2)\end{matrix}$where

-   -   k₀ is the normalization factor;    -   j is the signal number, where j=0, 1, 2, . . . , 15;    -   y(t) is a synthesized signal rendered by synthesizing a signal        sequence is accompanied by ICI with white Gaussian noise n(t)        that has a spectral power intensity N₀(y(t)=S_(j)+n(t));    -   P_(i)(S_(j)/y(t)) is the posterior probability of receiving the        signal S_(j) on the ith channel (the probability that the        received signal y(t) is S_(j));    -   P_(i)(i₁, i₂/y(t)) is the posterior probability of receiving        (i₁, i₂) on the ith channel (the probability that the received        signal y(t) is (i₁, i₂));    -   P_(apr)(S_(j)) is the prior probability of the received signal        S_(j);    -   P(y(t)/S_(ij)) is the probability that the transmitted code word        is S_(j) when the reception word is y(t), which is a conditional        probability; and    -   P(y(t)) is the probability of receiving y(t).

The probability P(y,(t)) of equation (2) is common to all the decisioncandidates and can therefore be disregarded. Further, the requirementfor judging received information is to find a candidate information forwhich the numerator or right side of the Equation (2) is maximized.

The prior probability Papr (S_(j))(j=0,1,2, . . . 15) of the firstchannel according to Equation (1) or Table 2 can be expressed as shownin Table 3 as a cross multiplication of the probabilities of twotransmission information signals S_(il)* i={1,2}, l={0,1, 2,3} ofadjacent channels. TABLE 3 P_(apr)(S₀) = P₁(S₃*) · P₂(S₃*) P_(apr)(S₁) =P₁(S₃*) · P₂(S₂*) P_(apr)(S₂) = P₁(S₃*) · P₂(S₀*) P_(apr)(S₃) = P₁(S₃*)· P₂(S₁*) P_(apr)(S₄) = P₁(S₂*) · P₂(S₃*) P_(apr)(S₅) = P₁(S₂*) ·P₂(S₂*) P_(apr)(S₆) = P₁(S₂*) · P₂(S₀*) P_(apr)(S₇) = P₁(S₂*) · P₂(S₁*)P_(apr)(S₈) = P₁(S₀*) · P₂(S₃*) P_(apr)(S₉) = P₁(S₀*) · P₂(S₂*)P_(apr)(S₁₀) = P₁(S₀*) · P₂(S₀*) P_(apr)(S₁₁) = P₁(S₀*) · P₂(S₁*)P_(apr)(S₁₂) = P₁(S₁*) · P₂(S₃*) P_(apr)(S₁₃) = P₁(S₁*) · P₂(S₂*)P_(apr)(S₁₄) = P₁(S₁*) · P₂(S₀*) P_(apr)(S₁₅) = P₁(S₁*) · P₂(S₁*)

In this notation, P_(apr)(S_(j)), j={0,1,2, . . . ,15} is the priorprobability of the transmission of the signal number j, P_(i)(S_(l)*) isthe transmission probability of signal S_(il)* on the ith channel.Accordingly, P₁(S_(l)*), l={0,1,2,3} is the transmission probability ofsignal S_(1l)* on the first channel. The transmission probabilitydepends on the data statistics for the transmission source of bits i₁,i₂ on the first channel and can be largely assumed to be equal to ¼ inan actual case. The probability P₂(S_(l)*) is the transmissionprobability of the QAM symbol of the second channel S_(2l)*, l={0,1,2,3}or the transmission probability of bits i₁ and i₂ on the second channel.It should be emphasized here that P₂(S_(l)*) is not equal to P₁(S_(l)*)and P₂(S_(l)*)≠¼.

In order to estimate P₂(S_(l)*), the posterior probability of thereceived signal when a special data set (i₁, i₂) is transmitted on thesecond channel is used. That is, P₂(S_(l)*)≈P₂((i₁,i₂)/y(t)) is used.This is the best estimation obtained in the case of an AWGN channel and,based on this supposition, Table 3 can be overwritten to produce Table4. TABLE 4 P_(apr)(S₀) = P₁(S₃*) · P₂((1, 1)/y(t)) P_(apr)(S₁) = P₁(S₃*)· P₂((1, 0)/y(t)) P_(apr)(S₂) = P₁(S₃*) · P₂((0, 1)/y(t)) P_(apr)(S₃) =P₁(S₃*) · P₂((0, 0)/y(t)) P_(apr)(S₄) = P₁(S₂*) · P₂((1, 1)/y(t))P_(apr)(S₅) = P₁(S₂*) · P₂((1, 0)/y(t)) P_(apr)(S₆) = P₁(S₂*) · P₂((0,1)/y(t)) P_(apr)(S₇) = P₁(S₂*) · P₂((0, 0)/y(t)) P_(apr)(S₈) = P₁(S₀*) ·P₂((1, 1)/y(t)) P_(apr)(S₉) = P₁(S₀*) · P₂((1, 0)/y(t)) P_(apr)(S₁₀) =P₁(S₀*) · P₂((0, 1)/y(t)) P_(apr)(S₁₁) = P₁(S₀*) · P₂((0, 0)/y(t))P_(apr)(S₁₂) = P₁(S₁*) · P₂((1, 1)/y(t)) P_(apr)(S₁₂) = P₁(S₁*) · P₂((1,0)/y(t)) P_(apr)(S₁₄) = P₁(S₁*) · P₂((0, 1)/y(t)) P_(apr)(S₁₅) = P₁(S₁*)· P₂((0, 0)/y(t))

Here, P_(i)((i₁,i₂)/y(t)), i={1, 2} is the probability that the data set(i₁, i₂) of the received signal y(t) of the ith channel is i₁=D₁, andi₂=D₂(D₁, D₂)={0, 1}). In order to simplify the notation,P_(i)((i₁/i₂)/y(t)) is written with the dependence of y(t) omittedtherefrom, such that P_(i)((i₁,i₂)/y(t))→P_(i)(i₁,i₂).

It is essential to determine the transmitted set i₁, i₂ on the firstchannel from the supplied input signal y(t). Because all the bits arestatistically independent, the decision with respect to i₁, i₂ can bemade independently and separately. The decision algorithm for i₁ will bedescribed first.

(C) Decision Algorithm for i₁

The posterior probability P₁(i₁/y(t)) of receiving bit i₁ of the firstchannel is obtained as the total of the posterior probabilities of thesignals S_(j) (j=0, 1, 2 . . . , 15) that correspond to the transmissionof the information bit i₁. The S_(j) dependence of i₂ can be removed byaveraging the signals from Table 2 including all possible i₂ for i₁. Thereception posterior probabilities P₁(i₁/y(t)) for the channels ofinterest from Table 2 are written as follows:P ₁(i ₁=1/y(t))=P ₁(11)·{P(S ₀)·P _(apr)(S ₀)+P(S ₁)·P _(apr)(S ₁)+P(S₂)·P _(apr)(S ₂)+P(S ₃)·P _(apr)(S ₃)}+P ₁(10)·{P(S ₄)·P _(apr)(S ₄)+P(S₅)·P _(apr)(S ₅)+P(S ₆)·P _(apr)(S ₆)+P(S ₇)·P _(apr)(S ₇)}  (3)P ₁(i ₁=0/y(t))=P ₁(00)·{P(S ₈)·P _(apr)(S ₈)+P(S ₉)·P _(apr)(S ₉)+P(S₁₀)·P _(apr)(S ₁₀)+P(S ₁₁)·P _(apr)(S ₁₁)}+P ₁(00)·{P(S ₁₂)·P _(apr)(S₁₂)+P(S ₁₃)·P _(apr)(S ₁₃)+P(S ₁₄)·P _(apr)(S ₁₄)+P(S ₁₅)·P _(apr)(S₁₅)}  (4)

The addition of Equations (3) and (4) serves to remove the dependency ofi₂ of the P₁(S_(j)/y(t))=P₁(i₁, i₂/y(t)) by averaging all i₂. Thesignals S₀ to S₇ from Table 2 are used to transmit i₁=1, while thesignals S₈, . . . S₁₅ are used to transmit i₁=0. In Equations (3) and(4), P₁(i₁, i₂) is the transmission probability that bits i₁ and i₂ onthe first channel will have a certain value. At this stage, this can beregarded as the prior probability of the transmission couple bits 11,10, 01, 00 on the first channel. Here, the following points should bere-emphasized. Even when the bits of this channel are independent and ofequal probability, the decisions for these bits are executedindependently and separately and it cannot be established that P₁(i₁,i₂) is ¼. While the decision with respect to i₁ is executed, anindependent decision with respect to i₂ can be estimated by the receiverwith a high degree of reliability. In other words, while the decisionwith respect to i₁ is executed, the following equation can be applied.P ₁(i ₁ ,i ₂)=P ₁(i ₁)·P ₁(i ₂=±1/y(t))=0.5·P ₁(i ₂ /y(t))  (5)

Here, P₁(i₂/y(t)) is the probability that bit i₂ on the first channelwill have a certain value D={0, 1}. The relationship of Table 3 cansubstitute P_(apr)(S_(j)) of Equations (3) and (4) according to thedirect relationship in Table 2 between 16 QAM symbol S_(il)*(t) and theinformation bits i₁ and i₂. The same assumption for bits i₁, i₂ derivesP₁(S_(l)*)=¼, l={0,1,2,3} and is the same for all the decisioncandidates. This element can therefore be ignored. Further,P₂(S_(l)*)=P₂(i₁,i₂). When this is considered, equations (3) and (4)become Equations (6) and (7) below.P ₁(i ₁=1/y(t))=P ₁(11)·{P(S ₀)·P ₂(11)+P(S ₁)·P ₂(10)+P(S ₂)·P₂(01)+P(S ₃)·P ₂(00)}+P ₁(10)·{P(S ₄)·P ₂(11)+P(S ₅)·P ₂(10)+P(S ₆)·P₂(01)+P(S ₇)·P ₂(00)}  (6)P(i ₁=0/y(t))=P ₁(01)·{P(S ₈)·P ₂(11)+P(S ₉)·P ₂(10)+P(S ₁₀)·P ₂(01)+P(S₁₁)·P ₂(00)}+P ₁(01)·{P(S ₁₂)·P ₂(11)+P(S ₁₃)·P ₂(10)+P(S ₁₄)·P₂(01)+P(S ₁₅)·P ₂(00)}  (7)

In the case of a maximum posterior probability receiver, code with thereceived information bit i₁ is determined in accordance with a logarithmfor the comparison result or threshold of the posterior probability.That is, the code (0 or 1) of the received information bit i₁ can bedetermined by means of a comparison of the sizes of the probabilitiesthat the received information bit i₁ will be 1 and 0 respectively or bymeans of a comparison of the difference between these logarithms and thethresholds thereof. Hence, the first bit i₁ of the first channel isfound by means of the following equation: $\begin{matrix}{{\frac{P_{1}\left( {i_{1} = {1/{y(t)}}} \right)}{P_{1}\left( {i_{1} = {0/{y(t)}}} \right)}\text{>/<}1}{or}} & \quad \\{{\ln\quad{P_{1}\left( {i_{1} = {1/{y(t)}}} \right)}} - {\ln\quad{P_{1}\left( {i_{1} = {0/{y(t)}}} \right)}\text{>/<}0}} & (8)\end{matrix}$

Here, when lnP₁(i₁=1/y(t)) and lnP₁(i₁=0/y(t)) in Equation (8) aremodified by considering the algebraic identity of the followingequation: $\begin{matrix}{{\ln\left( {{\mathbb{e}}^{X} + {\mathbb{e}}^{Y}} \right)} = {\frac{X + Y}{2} + {\ln\quad 2} + {\ln\quad{\cosh\left( \frac{X - Y}{2} \right)}}}} & (9)\end{matrix}$lnP₁(i₁=1/y(t)) and lnP₁(i₁=0/y(t)) become the following Equations (10)and (11) respectively: $\begin{matrix}\begin{matrix}{\begin{matrix}{\ln\quad P_{1}} \\\left( {i_{1} = {1\text{/}{y(t)}}} \right)\end{matrix} = {{{0.5 \cdot \ln}\quad{P_{1}(11)}} +}} \\{{0.5 \cdot \ln}\left\{ {{{P\left( S_{0} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{1} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{{P\left( S_{2} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{3} \right)} \cdot {P_{2}(00)}}} \right\} +} \\{{{0.5 \cdot \ln}\quad{P_{1}(10)}} +} \\{{0.5 \cdot \ln}\left\{ {{{P\left( S_{4} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{5} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{{P\left( S_{6} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{7} \right)} \cdot {P_{2}(00)}}} \right\} +} \\{\ln\quad\cosh\left\{ {0.5 \cdot \begin{pmatrix}{{\ln\quad{P_{1}(11)}} - {\ln\quad{P_{1}(10)}} +} \\{\ln\left( {{{P\left( S_{0} \right)}{P_{2}(11)}} + {{P\left( S_{1} \right)}{P_{2}(10)}} +} \right.} \\{\left. {{P\left( S_{2} \right){P_{2}(01)}} + {{P\left( S_{3} \right)}{P_{2}(00)}}} \right) -} \\{\ln\left( {{{P\left( S_{4} \right)}{P_{2}(11)}} + {{P\left( S_{5} \right)}{P_{2}(10)}} +} \right.} \\{{{P\left( S_{6} \right)}{P_{2}(01)}} + {{P\left( S_{7} \right)}{P_{2}(00)}}}\end{pmatrix}} \right\}}\end{matrix} & (10) \\\begin{matrix}{\begin{matrix}{\ln\quad P_{1}} \\\left( {i_{1} = {0\text{/}{y(t)}}} \right)\end{matrix} = {{{0.5 \cdot \ln}\quad{P_{1}(01)}} +}} \\{{0.5 \cdot \ln}\left\{ {{{P\left( S_{8} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{9} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{{P\left( S_{10} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{11} \right)} \cdot {P_{2}(00)}}} \right\} +} \\{{{0.5 \cdot \ln}\quad{P_{1}(00)}} +} \\{{0.5 \cdot \ln}\left\{ {{{P\left( S_{12} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{13} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{{P\left( S_{14} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{15} \right)} \cdot {P_{2}(00)}}} \right\} +} \\{\ln\quad\cosh\left\{ {0.5 \cdot \begin{pmatrix}{{\ln\quad{P_{1}(01)}} - {\ln\quad{P_{1}(00)}} +} \\{\ln\left( {{{P\left( S_{8} \right)}{P_{2}(11)}} + {{P\left( S_{9} \right)}{P(10)}} +} \right.} \\{\left. {{P\left( S_{10} \right){P_{2}(01)}} + {{P\left( S_{11} \right)}{P_{2}(00)}}} \right) -} \\{\ln\left( {{{P\left( S_{12} \right)}{P_{2}(11)}} + {{P\left( S_{13} \right)}{P_{2}(10)}} +} \right.} \\{{{P\left( S_{14} \right)}{P_{2}(01)}} + {{P\left( S_{15} \right)}{P_{2}(00)}}}\end{pmatrix}} \right\}}\end{matrix} & (11)\end{matrix}$

For example, supposing that, for lnP₁(i₁=1/y(t)), the first term on theright side of Equation (6) is e^(X) and the second term on the rightside is e^(Y), that is,e ^(X) =P ₁(11)·{P(S ₀)·P ₂(11)+P(S ₁)·P ₂(10)+P(S ₂)·P ₂(01)+P(S₃)·P₂(00)}e ^(Y) =P ₁(10)·{P(S ₄)·P ₂(11)+P(S ₅)·P ₂(10)+P(S ₆)·P ₂(01)+P(S ₇)·P₂(00)},this yields:X=ln P ₁(11)+ln{P(S ₀)·P ₂(11)+P(S₁)·P ₂(10)+P(S ₂)·P ₂(01)+P(S ₃)·P₂(00)}Y=ln P ₁(10)+ln{P(S ₄)·P ₂(11)+P(S ₅)·P ₂(10)+P(S ₆)·P ₂(01)+P(S ₇)·P₂(00)}.

If X and Y are substituted into Equation (9), lnP₁(i₁=1/y(t)) ofEquation (10) is found. Likewise, for lnP₁(i₁=0/y(t)), if the first termon the right side of Equation (7) is e^(X) and the second term on theright side is e^(Y), Equation (11) is obtained. Further, if lncosh {•}in Equations (10) and (11) is omitted for the sake of simplification,(reconsidered thereafter),ΔlnP₁(i₁=1/y(t))=ΔlnP₁(i₁=1/y(t))−ΔlnP₁(i₁=0/y(t)) in Equation (8)becomes Equation (12).Δ ln P ₁(i ₁ /y(t))=ln P(i ₁=1/y(t))−ln P(i ₁=0/y(t))=0.5·(ln P ₁(11)+lnP ₁(10)−ln P ₁(01)−ln P ₁(00))+ln{P(S ₀)·P ₂(11)+P(S ₁)·P ₂(10)+P(S ₂)·P₂(01)+P(S ₃)·P ₂(00)}+ln{P(S ₄)·P ₂(11)+P(S ₅)·P ₂(10)+P(S ₆)·P₂(01)+P(S ₇)·P ₂(00)}−ln{P(S ₈)·P ₂(11)+P(S ₉)·P ₂(10)+P(S ₁₀)·P₂(01)+P(S ₁₁)·P ₂(00)}−ln{P(S ₁₂)·P ₂(11)+P(S ₁₃)·P ₂(10)+P(S ₁₄)·P₂(01)+P(S₁₅)·P ₂(00)}  (12)

If Equation (12) is modified further by considering the algebraicidentity of Equation (9) and lncosh {•} is reconsidered, Equation (13)is obtained. For the method of deriving Equation (13), kindly refer toappendix A. $\begin{matrix}\begin{matrix}{\begin{matrix}{\Delta\quad\ln\quad P_{1}} \\{\quad\left( {i_{1}/{y(t)}} \right)}\end{matrix} = {{\Delta\quad\ln\quad{P_{1}\left( i_{1} \right)}} - {4 \cdot d \cdot y} +}} \\{{0.25 \cdot \begin{pmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{01}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{01}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{32}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{45}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{76}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix}} +} \\{{0.50 \cdot \begin{pmatrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{02}} - {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{810}} + {\Delta\quad E_{911}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} +}\end{matrix} \\\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{46}} - {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{1412}} + {\Delta\quad E_{1513}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{matrix}\end{pmatrix}} +} \\{0.25\begin{pmatrix}{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - \left( {{\Delta\quad E_{04}} + {\Delta\quad E_{15}} + {\Delta\quad E_{26}} + {\Delta\quad E_{37}}} \right) +} \right.} \right.} \\{\left. \left. {\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}} \right) \right\} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + \left( {{\Delta\quad E_{128}} + {\Delta\quad E_{139}} + {\Delta\quad E_{1410}} + {\Delta\quad E_{1511}}} \right) +} \right.} \right.} \\\left. \left. {\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}} \right) \right\}\end{pmatrix}}\end{matrix} & (13)\end{matrix}$

In Equation (13), the amplitude of the received signal is unchanged overcycle T for the sake of simplifying the equation. Hence, the referencesignal S_(j) (t) is also constant over this period. Further, y andΔE_(mn) below are introduced to Equation (13). That is, according toEquation (2), $\begin{matrix}{{\ln\quad{P\left( {S_{j}/{y(t)}} \right)}} = {{\frac{2}{N_{0}}{\int_{0}^{T}{{{y(t)} \cdot {S_{j}(t)}}\quad{\mathbb{d}t}}}} - {\frac{E_{j}}{N_{0}}\quad\left( {{j = 0},1,2,{\ldots\quad 15}} \right)}}} & (14)\end{matrix}$is established. However, E_(j) is the energy of signal S_(j), such that:E _(j)=∫₀ ^(T) S _(j)(t)² dt

The first term on the right side of Equation (14) is a correlationbetween the signal y(t) and the reference signal S_(j). In order tosimplify the notation in Equation (14), y is introduced as follows:$y->{\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}\quad{\mathbb{d}t}}}}$

Accordingly, Equation (14) becomes: $\begin{matrix}{{\ln\quad{P\left( {S_{j}/{y(t)}} \right)}} = {{\ln\quad{P\left( S_{j} \right)}} = {{y \cdot {S_{j}(t)}} - \frac{E_{j}}{N_{0}}}}} & (14)^{\prime}\end{matrix}$

Further, the energy difference ΔE_(mn) between signals S_(m) and S_(n)is introduced and defined as:ΔE _(mn)=(E _(m) −E _(n))/N ₀

The following equations are established according to the energydifferences from Table 2.ΔE ₀₁ =ΔE ₁₀₁₁=(12α+8α²)·d ² ; ΔE ₃₂ =ΔE ₉₈=(12α−8α²)·d ²ΔE ₄₅ =ΔE ₁₅₁₄=(4α+8α²)·d ² ; ΔE ₇₆ =ΔE ₁₂₁₃=(4α−8α²)·d ²ΔE ₀₂ +ΔE ₁₃ =ΔE ₈₁₀ +ΔE ₉₁₁=48α·d ² ; ΔE ₄₆ +ΔE ₅₇ =ΔE ₁₄₁₂ +ΔE₁₅₁₃=16α·d ²ΔE ₀₄ +ΔE ₁₅ +ΔE ₂₆ +ΔE ₃₇ =ΔE ₁₂₈ +ΔE ₁₃₉ +ΔE ₁₄₁₀ +ΔE ₁₅₁₁=32·d²  (15)

For example, ΔE₀₁=(E₀−E₁)=(−3d−3da)²−(−3d−da)²=(12a−8a2)².

The following nonlinear function for Equation (13): $\begin{matrix}{{F\left( {x,{\Delta\quad E}} \right)} = {{\ln\quad\cosh\left\{ \frac{x - {\Delta\quad E}}{2} \right\}} - {\ln\quad\cosh\left\{ \frac{x + {\Delta\quad E}}{2} \right\}}}} & (16)\end{matrix}$can be written as a limiter with a linear region. The limit level of thenonlinear function is dependent on the S/N ratio (noise spectral powerintensity N₀) and the energy difference ΔE_(mn) between the signalsS_(m) and S_(n). FIG. 8 shows a nonlinear function F(x,ΔE) when thedifference ΔE_(mn) is the parameter. The relation of the followingequation $\begin{matrix}{{F\left( {x,{\sum\limits_{i}{\Delta\quad E_{i}}}} \right)} = {{F\left( {x,{\Delta\quad E_{1}}} \right)} + {F\left( {x,{\Delta\quad E_{2}}} \right)} + {F\left( {x,{\Delta\quad E_{3}}} \right)} + \cdots}} & (17)\end{matrix}$is established for the nonlinear function. FIG. 9 shows thecharacteristics of the nonlinear functions F(x, ΔE₁+ΔE₂), F(x, ΔE₁),F(x, ΔE₂). When the third term on the right side of Equation (13) ismodified by using the relation of Equation (17), Equation (18) isproduced. $\begin{matrix}{\begin{pmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{01}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{01}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix} = \begin{matrix}{{\ln\quad\cosh\left\{ {{0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{\Sigma 1}}} \right)} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right\}} -} \\{\ln\quad\cosh\left\{ {{0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{\Sigma 1}}} \right)} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right\}}\end{matrix}} & (18)\end{matrix}$

Further, when the fourth term on the right side of Equation (13) ismodified by using the relation in Equation (17), Equation (19) isproduced. $\begin{matrix}{\begin{pmatrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{02}} - {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{810}} + {\Delta\quad E_{911}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} +}\end{matrix} \\\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{46}} - {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{1412}} + {\Delta\quad E_{1513}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{matrix}\end{pmatrix} = \begin{matrix}{{\ln\quad\cosh\left\{ {{0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{\Sigma 2}}} \right)} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right\}} -} \\{\ln\quad\cosh\left\{ {{0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{\Sigma 2}}} \right)} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right\}}\end{matrix}} & (19)\end{matrix}$

The above equation is the probability ΔlnP₁(i₁/y(t)) of the first bit i₁of the first channel. If this probability is greater than 0, i₁=“1” andif this probability is smaller than 0, i₁=“0”.

(D) First Channel/First Bit i₁ Turbo Receiver

FIG. 10 is a block diagram of a turbo receiver that estimates theprobability ΔlnP₁(i₁/y(t)) of the first bit i₁ of the first channel bymeans of Equation (13) in which blocks are rendered by using therelations of Equations (18) and (19). The constitution of the blocks canbe simplified by using the relations of Equations (18) and (19).

In a broad classification, the first channel/first bit i₁ turbo receiveris constituted by a receiver portion 31 a and a symbol decision unit 32,wherein the receiver portion 31 a comprises a correlation unit (may alsobe a matched filter) 61, an other channel decision result operation unit62, an own channel second bit decision result operation unit 63, anonlinear unit 64, a coefficient multiplication unit 65 and asynthesizer unit 66.

A first multiplication unit 61 a, first integrator 61 b, secondmultiplication unit 61 c; and second integrator 61 d of the correlationunit 61 integrate the results of multiplying the received signal y(t) bypredetermined reference signals S₀ to S₁₅ and the multiplication unit 61e multiplies the output −4dy of the first integrator 61 b by a. Theother channel decision result operation unit 62 comprises adders 62 aand 62 b, wherein the adder 62 a adds the probability ΔlnP₂(i₂) of thesecond bit of the second channel to the output signal of the secondintegrator 61 d and the adder 62 b adds the probability ΔlnP₂(i₁) of thefirst bit of the second channel to the output signal of the firstintegrator 61 b that has been multiplied by a. The own channel decisionresult operation unit 63 comprises an adder 63 a, wherein the adder 63 aadds the probability Δln₁(i₂) of the second bit of the first channel tothe output signal of the second integrator 61 d.

The nonlinear unit 64 a executes a nonlinear calculation of the thirdterm on the right side of Equation (13), the nonlinear unit 64 bexecutes a nonlinear calculation of the fourth term on the right side ofEquation (13), and the nonlinear unit 64 c executes a nonlinearcalculation of the fifth term on the right side of Equation (13). Eachof the multiplication units 65 a to 65 c of thecoefficient-multiplication unit 65 calculates the third to fifth termson the right side of Equation (13) by multiplying the output of thenonlinear units 64 a to 64 c by the constants 0.25, 0.50, and 0.25respectively, the synthesizer unit 66 adds the first to fifth terms onthe right side of Equation (13) and outputs the probabilityΔlnP₁(i₁/y(t)) of the first bit i₁ of the first channel, and the symboldecision unit 32 decides whether the code of the first bit i₁ is “+” or“−”, that is, “0” or “1”, depending on whether the probabilityΔlnP₁(i₁/y(t)) is greater or smaller than 0.

The probability ΔlnP₁(i₁/y(t)) is fed back to the turbo receiver of thesecond bit i₂ and to the turbo receivers of the first and second bits ofthe second channel. Although the first term on the right side ofEquation (13) was omitted earlier on account of being small, ifnecessary, ΔlnP₁(i₁) can also be added by the synthesizer unit 66.

Further, the constitution of FIG. 10 can also be used when receiving thefirst bit q₁ of the Quadrature component of the first channel. Theconstitution of FIG. 10 can also be used when receiving the first bitsi₁ and q₁ of the common mode component and Quadrature component of thesecond channel respectively.

(E) Decision Algorithm for Second Bit i₂

Similarly to the first bit i₁, the reception posterior probabilityP₁(i₂/y(t)) of the first channel/second bit is obtained as the sum ofthe posterior probabilities of the signals S_(j) corresponding to thetransmission of the information bit i₂. The dependency of i₁ on S_(j)can be removed by averaging the signals for all the possible i₁ fromTable 2. The reception posterior probabilities P₁(i₂/y(t)) of thechannels of interest from Table 2 are written as below.P ₁(i ₂=1/y(t))=P ₁(11)·{P(S ₀)·P _(apr)(S ₀)+P(S ₁)·P _(apr)(S ₁)+P(S₂)·P _(apr)(S ₂)+P(S ₃)·P _(apr)(S ₃)}+P ₁(01)·{P(S ₈)·P _(apr)(S ₈)+P(S₉)·P _(apr)(S ₉)+P(S ₁₀)·P _(apr)(S ₁₀)+P(S ₁₁)·P _(apr)(S ₁₁)}  (20)P ₁(i ₁=0/y(t))=P ₁(10)·{P(S ₄)·P _(apr)(S ₄)+P(S ₅)·P _(apr)(S ₅)+P(S₆)·P _(apr)(S ₆)+P(S ₇)·P _(apr)(S ₇)}+P ₁(00)·{P(S ₁₂)·P _(apr)(S₁₂)+P(S ₁₃)·P _(apr)(S ₁₃)+P(S ₁₄)·P _(apr)(S ₁₄)+P(S ₁₅)·P _(apr)(S₁₅)}  (21)

Care must be taken to make the combinations of the signals S_(j) inEquations (20) and (21) different from those in Equations (3) and (4).Here, the same signal notation system as in Table 2 is used. Similarlyto Equations (3) and (4), the addition of Equations (20) and (21) servesto remove the dependency of i₁ in P₂(S_(j)/y(t))=P₂(i₁,i₂/y(t)) byaveraging P₂(S_(j)/y(t)) for all the i₁. The signals S₀ to S₃ and S₈ toS₁₁ from Table 2 are used to transmit i₂=1, while signals S₄ to S₇ andS₁₂ to S₁₅ are used to transmit i₂=0.

The following equation is obtained for bit i₁ as per Equations (6) and(7) according to the direct relationship in Table 3 between 16 QAMsymbol P₁(S_(l)*), l={0,1,2,3} and the information bits i₁ and i₂.P ₁(i ₂=1/y(t))=P ₁(11)·{P(S ₀)·P ₂(11)+P(S ₁)·P ₂(10)+P(S ₂)·P₂(01)+P(S ₃)·P ₂(00)}+P ₁(10)·{P(S ₈)·P ₂(11)+P(S ₉)·P ₂(10)+P(S ₁₀)·P₂(01)+P(S ₁₁)·P ₂(00)}  (22)P ₁(i ₂=0/y(t))=P ₁(01)·{P(S ₄)·P ₂(11)+P(S ₅)·P ₂(10)+P(S ₆)·P₂(01)+P(S ₇)·P ₂(00)}+P ₁(00)·{P(S ₁₂)·P ₂(11)+P(S ₁₃)·P ₂(10)+P(S ₁₄)·P₂(01)+P(S ₁₅)·P ₂(00)}  (23)

Here, attention should be drawn to the fact that Equations (22) and (23)are the same as Equations (6) and (7). The difference lies only in thecombination. Hence, all the results obtained in appendix A can also beadopted for Equations (22) and (23). The following equations areobtained by applying the decision rules of Equation (8) for the secondbit of the first channel (see appendix A). $\begin{matrix}\begin{matrix}{{\Delta\quad\ln\quad{P_{1}\left( {i_{2}/{y(t)}} \right)}} = {{\ln\quad{P_{1}\left( {i_{2} = {{1/y}(t)}} \right)}} - {\ln\quad{P_{1}\left( {i_{2} = {{0/y}(t)}} \right)}}}} \\{= {{0.5 \cdot \left( {{\ln\quad{P_{1}(11)}} + {\ln\quad{P_{1}(01)}} - {\ln\quad{P_{1}(10)}} - {\ln\quad{P_{1}(00)}}} \right)} +}} \\{\ln\left\{ {{{P\left( S_{0} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{1} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{{P\left( S_{2} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{3} \right)} \cdot {P_{2}(00)}}} \right\} +} \\{\ln\left\{ {{{P\left( S_{8} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{9} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{{P\left( S_{10} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{11} \right)} \cdot {P_{2}(00)}}} \right\} -} \\{\ln\left\{ {{{P\left( S_{4} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{5} \right)} \cdot {P_{2}(10)}} +} \right.} \\{\left. {{P{\left( S_{6} \right) \cdot {P_{2}(01)}}} + {{P\left( S_{7} \right)} \cdot {P_{2}(00)}}} \right\} -} \\{\ln\left\{ {{{P\left( S_{12} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{13} \right)} \cdot {P_{2}(10)}} +} \right.} \\\left. {{P{\left( S_{14} \right) \cdot {P_{2}(01)}}} + {{P\left( S_{15} \right)} \cdot {P_{2}(00)}}} \right\}\end{matrix} & (24) \\\begin{matrix}{\begin{matrix}{\Delta\quad\ln\quad P_{1}} \\{\quad\left( {i_{2}/{y(t)}} \right)}\end{matrix} = {{\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}} - {8 \cdot {d^{2}/N_{0}}} +}} \\{{0.25 \cdot \begin{pmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{01}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{32}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{76}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{01}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{45}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix}} +} \\{{0.50 \cdot \begin{pmatrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{02}} - {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{46}} + {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} +}\end{matrix} \\\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{810}} - {\Delta\quad E_{911}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{1412}} + {\Delta\quad E_{1513}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{matrix}\end{pmatrix}} +} \\{{\ln\left\{ {\cosh\begin{Bmatrix}{{0.5\begin{pmatrix}{{\Delta\quad\ln\quad{P_{1}\left( i_{1} \right)}} - {6 \cdot d \cdot y} + {0.5 \cdot (}} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{01}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{01}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{32}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\\left. {\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} \right)\end{pmatrix}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{02}} - {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{02}} + {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{Bmatrix}} \right\}} -} \\{\ln\left\{ {\cosh\begin{Bmatrix}{{0.5\begin{pmatrix}{{\Delta\quad\ln\quad{P_{1}\left( i_{1} \right)}} - {2 \cdot d \cdot y} + {0.5 \cdot (}} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{45}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{76}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\\left. {\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} \right)\end{pmatrix}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{46}} - {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{46}} + {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{Bmatrix}} \right\}}\end{matrix} & (25)\end{matrix}$

The decision expression for the second bit of Equation (25) can beregarded as complex in comparison with the decision expression for thefirst bit (Equation (13)). However, the linear part comprisessymmetrical opposite terms as is clear from Equation (25). In order toavoid additional complexity, several approximations are introduced.First, the sum of two nonlinear functions of an actual argument x withsymmetrical opposite terms as shown in Equation (26) may be considered.F ₁(x, ΔE ₁ , ΔE ₂)=log{cosh{0.5(x−ΔE ₁)}}−log{cosh{0.5(x+ΔE ₂)}}F ₂(x, ΔE ₁ , ΔE ₂)=log{cosh{0.5(x+ΔE ₁)}}−{cosh{0.5(x−ΔE ₂)}}+F _(Σ)(x, ΔE ₁ , ΔE ₂)=F ₁(x, ΔE ₁ , ΔE ₂)+F ₂(x, ΔE ₁ , ΔE ₂)  (26)

FIG. 11 shows the transmission function of the nonlinear unit FS(x, ΔE₁,ΔE₂) in the case ΔE₁=−5 and ΔE₂=−2. As can be seen from FIG. 11, thelarger the argument x, the closer FS(x, ΔE₁, ΔE₂) is to zero.

Here, the argument x of Equation (26) corresponds to the correlationoutput signal$y\left( {y->{\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}\quad{\mathbb{d}t}}}}} \right)$of the decision expression of Equation (25). Hence, when the S/N ratiois high (when N₀→0 and 2/N₀→8), the function FS (x, ΔE₁, ΔE₂) is thenequal to zero and the linear terms of Equation (25) can be approximatedas follows: $\begin{matrix}\begin{matrix}{{\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}} - {8 \cdot {d^{2}/N_{0}}} +} \\{{0.25 \cdot \begin{pmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{01}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{32}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{76}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +}\end{matrix} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{01}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{45}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix}} +} \\{{0.50 \cdot \begin{pmatrix}\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{02}} - {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{46}} + {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} +}\end{matrix} \\\begin{matrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{810}} - {\Delta\quad E_{911}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{1412}} + {\Delta\quad E_{1513}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{matrix}\end{pmatrix}} \approx} \\{{\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}} - {8 \cdot {d^{2}/N_{0}}}}\end{matrix} & (27)\end{matrix}$

Further, the decision expression ΔlnP₁(i₂) is ultimately the followingexpression: $\begin{matrix}\begin{matrix}{\begin{matrix}{\Delta\quad\ln\quad P_{1}} \\{\quad\left( {i_{2}/{y(t)}} \right)}\end{matrix} = {{\ln\quad{P_{1}\left( {i_{2} = 1} \right)}} - {\ln\quad{P_{1}\left( {i_{2} = 0} \right)}}}} \\{= {{\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}} - {8 \cdot {d^{2}/N_{0}}} +}} \\{{\ln\left\{ {\cosh\begin{Bmatrix}{{0.5\begin{pmatrix}{{\Delta\quad\ln\quad{P_{1}\left( i_{1} \right)}} - {6 \cdot d \cdot y} + {0.5 \cdot (}} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} - {\Delta\quad E_{01}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} + {\Delta\quad E_{01}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} - {\Delta\quad E_{32}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\\left. {\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} + {\Delta\quad E_{32}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} \right)\end{pmatrix}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{02}} - {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{02}} + {\Delta\quad E_{13}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{Bmatrix}} \right\}} -} \\{\ln\left\{ {\cosh\begin{Bmatrix}{{0.5\begin{pmatrix}{{\Delta\quad\ln\quad{P_{1}\left( i_{1} \right)}} - {2 \cdot d \cdot y} + {0.5 \cdot (}} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} - {\Delta\quad E_{45}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} + {\Delta\quad E_{45}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} - {\Delta\quad E_{76}} - {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} -} \\\left. {\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha\quad{dy}} + {\Delta\quad E_{76}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} \right)\end{pmatrix}} +} \\{{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} - {\Delta\quad E_{46}} - {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}} -} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 4}{\alpha \cdot d \cdot y}} + {\Delta\quad E_{46}} + {\Delta\quad E_{57}} + {\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}\end{Bmatrix}} \right\}}\end{matrix} & (28)\end{matrix}$

(F) First Channel/Second Bit i₂ Turbo Receiver

FIG. 12 is a block diagram of a turbo receiver that estimates theprobability ΔlnP₁(i₂/y(t)) of the second bit i₂ of the first channel bymeans of Equation (28), which, in a broad classification, is constitutedby a receiver portion 31 b and a symbol decision unit 33, wherein thereceiver portion 31 b comprises a correlation unit (may be a matchedfilter) 71, an other channel decision result operation unit 72, an ownchannel first bit decision result operation unit 73, first to thirdnonlinear units 74 to 76, a calculation unit 77, and an adder 78.

The first multiplication unit 71 a, first integrator 71 b, secondmultiplication unit 71 c, second integrator 71 d, third multiplicationunit 71 e and third integrator 71 f of the correlation unit 71 integratethe results of multiplying the received signal y(t) by predeterminedreference signals S₀ to S₁₅. The other channel decision result operationunit 72 comprises adders 72 a and 72 b, wherein the adder 72 a adds theprobability ΔlnP₂(i₂) of the second bit of the second channel to theoutput signal of the second integrator 71 d and the adder 72 b adds theprobability ΔlnP₂(i₁) of the first bit of the second channel to theoutput signal of the third integrator 71 f.

The first nonlinear unit 74 a executes a first nonlinear calculation inthe third term on the right side of Equation (28) and the other firstnonlinear unit 74 b executes a first nonlinear calculation in the fourthterm on the right side of Equation (28). The second nonlinear unit 75 aexecutes a first nonlinear calculation in the third term on the rightside of Equation (28) and the other second nonlinear unit 75 b executesa second nonlinear calculation in the fourth term on the right side ofEquation (28). A multiplier 77 a of the multiplication unit 77calculates −6dy in the third term on the right side of Equation 28; anadder 77 c adds −6dy, the output of the first nonlinear unit 74 a andthe output of the second nonlinear unit 75 a; a multiplier 77 bcalculates −2dy in the fourth term on the right side of Equation (28);and the adder 77 d adds −2dy, the output of the first nonlinear unit 74b and the output of the second nonlinear unit 75 b.

The own channel decision result operation unit 73 outputs signals A andB by adding the probability ΔlnP₁(i₁) of the first bit of the firstchannel to the output signal of the adders 77 c and 77 d. The thirdnonlinear unit 76 executes the nonlinear calculation ln cosh[A]+lncosh[B], the adder 78 outputs the probability ΔlnP₁(i₂/y(t)) by adding−8d²/N₀ to the output of the third nonlinear unit 76, and the symboldecision unit 33 decides whether the code of the second bit i₂ is “+” or“−”, that is, “0” or “1”, depending on whether the probabilityΔlnP₁(i₂/y(t)) is greater or smaller than 0.

The probability ΔlnP₁(i₂/y(t)) is fed back to the turbo receiver portionof the first bit i₁ and to the turbo receiver portions of the first andsecond bits of the second channel. Although the first term of Equation(28) was omitted earlier on account of being small, if necessary, theadder 78 can be constituted such that ΔlnP₁(i₂)−8d²/N₀ is added insteadof −8d²/N₀.

Further, the constitution of FIG. 12 can also be used when receiving thesecond bit q₂ of the Quadrature component of the first channel. Theconstitution of FIG. 12 can also be used when receiving the second bitsi₂ and q₂ of the common mode component and Quadrature component of thesecond channel respectively.

(G) Overall Constitution of Turbo Receiver Portion

FIG. 13 is a constitutional view of the receiver of the first and secondchannels in which the same numerals are assigned to the same parts as inFIGS. 7, 10, and 12. The receiver unit 30 of the first channel and thereceiver unit 40 of the second channel have the same constitution. Thatis, the first channel/first bit turbo receiver portion (31 a, 32) andthe second channel/first bit turbo receiver portion (41 a, 42) have thesame constitution. Further, the first channel/second bit turbo receiverportion (31 b, 33) and second channel/second bit turbo receiver portion(41 b, 43) have the same constitution.

The first channel/first bit turbo receiver portion 31 a estimates thefirst channel/first bit probability ΔlnP₁(i₁/y(t)) by using the firstchannel/second bit probability ΔlnP₁(i₂) and the probabilities ΔlnP₂(i₁)and ΔlnP₂(i₂) of the first and second bits of the second channelrespectively and the symbol decision unit 32 judges the firstchannel/first bit on the basis of the probability ΔlnP₁(i₁/y(t)).

The first channel/second bit turbo receiver 31 b estimates the firstchannel/second bit probability ΔlnP₁(i₂/y(t)) by using the firstchannel/first bit probability ΔlnP₁(i₁) and the probabilities ΔlnP₂(i₁)and ΔlnP₂(i₂) of the first and second bits of the second channelrespectively and the symbol decision unit 33 judges the firstchannel/second bit on the basis of the probability ΔlnP₁(i₂/y(t)).

Likewise, the second channel/first bit turbo receiver portion 41 aestimates the second channel/first bit probability ΔlnP₂(i₁/y(t)) byusing the second channel/second bit probability ΔlnP₂(i₂) and theprobabilities ΔlnP₁(i₁) and ΔlnP₁(i₂) of the first and second bits ofthe first channel respectively and the symbol decision unit 42 judgesthe second channel/first bit on the basis of the probabilityΔlnP₂(i₁/y(t)).

The second channel/second bit turbo receiver portion 41 b estimates thesecond channel/second bit probability ΔlnP₂(i₂/y(t)) by using the secondchannel/first bit probability ΔlnP₂(i₁) and the probabilities ΔlnP₁(i₁)and ΔlnP₁(i₂) of the first and second bits of the first channelrespectively and the symbol decision unit 43 judges the secondchannel/second bit on the basis of the probability ΔlnP₂(i₂/y(t)).

Although the demodulation of the first and second bits of an in-phasecomponent were described earlier, the first and second bits of aQuadrature component can also be demodulated and outputted by means ofthe same constitution.

(H) Turbo Algorithm

Equations (13) and (28) define the constitution of the optimal receiverfor a 16 QAM signal with ICI. As can be seen from Equations (13) and(28), when the codes of the transmitted first and second bits aredetermined, decision information (prior probability logarithmdifference) that was created beforehand for the first and second bits i₁and i₂ respectively and decision information of the adjacent channel areemployed. In equation (13), which is a decision expression for the firstchannel, this information is ΔlnP₁(i₁), ΔlnP₂(i₂), and ΔlnP₂(i₁), whichdenote the logarithm difference of the posterior probability (softdecision) of whether the codes of the transmitted bits of the first andsecond channels are “+” or “−”. Because all the calculations areperformed serially, iterative counting to adopt the latest posteriorprobability from the first and second channels is possible during theprocessing according to Equation (13). The turbo connection between thetwo-channel soft decisions is as shown in FIG. 13.

The proposed algorithm is analogous to the turbo decoder method of M. C.Valeniti and B. D. Woerner, “Variable latency turbo codes for wirelessmultimedia applications,” Proc, Int. Symposium on Turbo codes andRelated Topics., Brest, France, September 1997, pp 216-219, which wasdesigned for turbo codes.

Due to the similarity with the turbo decoder, the algorithm of thepresent invention shall be called a turbo receiver. The well-knownViterbi phrase that information that is beneficial to a decision is notdiscarded at all until all decisions are complete is extremely good andsuited to the turbo receiver of the present invention.

Because all the calculations are performed sequentially for eachchannel, iterative counting that adopts the latest posterior probabilityestimation values from the adjacent channel is performed. In the turbodecoder, each decoder passes information to the other decoder and thenclosely examines the posterior probabilities that are estimatedsequentially by using information that is derived from the otherdecoder. Likewise, with the algorithm of the present invention,information that is derived following nonlinear processing from thefirst subchannel is used to examine closely the estimated posteriorprobability of the second channel, while information that is derivedfrom the second channel is similarly used to examine closely theestimated posterior probability of the first channel. As in the case ofan iterative turbo decoder, the algorithm of the present inventionperforms one or more iterations before making a final decision withrespect to a received information symbol. If, in the case of a turboreceiver, individual decoder outputs are in the hard bit decision (harddecision) format, there is only a slight benefit to be derived fromsharing the information. The hard bit decision is analogous to thedecision feedback equalizer proposed for the purpose of ICI cancellationby Viterbi and Fazel in Viterbi and K. Fazel, “How to combat long echoesin OFDM transmission schemes: Subchannel equalization or more powerfulchannel coding,” Proc. IEEE Globecom '95, Singapore, November 1995, pp.2069-2074. However, according to the present invention, the hard bitdecision is performed only in the final iteration.

This structural similarity exists for the following reason. That is,with a turbo receiver, as in the case of turbo codes, the sameinformation is transmitted on a subchannel with non-correlative noisedue to the existence of ICI. The estimation of the posterior probability(or reliability of the determination) can be improved by using theestimated posterior probability derived from the other subchannel inaccordance with the handling of this non-correlative noise.

As per an iterative turbo decoder, the algorithm of the presentinvention performs one or more iterations before making the finaldecision with respect to the received information. Further, in theinitial first channel/first bit step, that is, when the decision resultfor the second bit of the first channel and the decision result for thefirst and second bits from the second channel cannot be used, if thedata is a probability variable with a uniform distribution, theprobabilities can be established, for the first channel, as:P ₁(i ₂=+1/y(t))=½, P ₁(i ₂=0/y(t))=½P ₂(i ₁=+1/y(t))=½, P ₂(i ₁=0/y(t))=½P ₂(i ₂=+1/y(t))=½, P ₂(i ₂=0/y(t))=½.

These settings are the optimum settings. Hence, in the first step of thefirst channel, suppose that the differences between posteriorprobabilities ΔlnP₁(i₂), ΔlnP₂(i₁) and ΔlnP₂(i₂) of Equation (13) arezero. The calculation of Equation (13) based on the assumption thatΔlnP₁(i₂)=0, ΔlnP₂(i₁)=0 and ΔlnP₂(i₂)=0 provides an initial estimatefor ΔlnP₁(i₁) and ΔlnP₁(i₂), which are the estimation targets for thefirst channel. Likewise, according to the algorithm of Equation (28) ofthe present invention, the second channel adopts the posteriorprobabilities ΔlnP₁(i₁)=0 and ΔlnP₁(i₂)=0 during the initial iteration.In the second step, in order to calculate the new estimation posteriorprobabilities ΔlnP₁(i₁) and ΔlnP₁(i₂) for the first channel, the valuesof ΔlnP₂(i₁) and ΔlnP₂(i₂) obtained in the previous step must be appliedto Equation (28), which is the decision expression. In accordance withthis method, the output of a channel receiver is used as the priorprobability of the other receiver.

(I) Simulation Results

FIG. 14 is an explanatory diagram of constellations of the first channelwith different points of the communication system shown in FIG. 7 where16 QAM is adopted and the S/N ratio=10 dB. Further, the cross-channelleak coefficients are α₂₁=0.25 and α₁₂=0.25. (A) is a constellation ofthe original 16 QAM signal; (B) is a constellation of an ICI-free 16 QAMsignal with noise where S/N ratio=10 dB; (C) is a constellation of thereceived signal (16 QAM signal that has deteriorated due to noise); (D)is a constellation of the initial 16 QAM signal of the presentinvention; and (E) is a constellation of a 16 QAM signal that hasundergone two turbo iterations.

It is clear from an analysis of (B), (C), and (D) that the effects ofICI decrease following the turbo processing of the present invention.That is, the constellation that has undergone two turbo iterations (seeE) is extremely close to ICI-free transmission (see B) that hasdeteriorated only due to Gaussian noise.

As detailed earlier, the receiver of the present invention adopts anonlinear unit and crossfeed in order to improve the estimation of theposterior probability. This constitution signifies that, though notimpossible, an analysis of the BER performance is extremely difficult.Hence, a computer simulation was carried out in order to demonstratethat the nonlinear signal processing of the present invention wassuperior to that of a classical matched filter receiver.

FIGS. 15 and 16 show the average BER performance (written as 2Turbo) ofthe first bit i₁ and second bit i₂ of the receiver of the presentinvention as the function 2Eb/N₀ based on Equations (13) and (28)respectively. Eb/N₀ is the ratio between the background noise powerspectral intensity N₀ per bit and the average received signal energy Eb.The performance in each case is the result of 16 QAM transmission via anAWGN channel in a case where α₁=α₂=0.25. 2Turbo is the result of thepresent invention following two turbo iterations. By way of reference,the results of a simulation (ICI-free) in a case where no ICI exists andα₁₂=α₂₁=0 are shown in FIGS. 15 and 16. As a further reference, theresults of a BER simulation (written as REF) when the ICI of a matchedfilter receiver calculated by using the formula of Equation (29) doesnot exist are shown. $\begin{matrix}{{{{{BER}\left( i_{1} \right)} = {\frac{1}{2}\left( {{Q\left( \sqrt{\frac{E_{0}}{5N_{0}}} \right)} + {Q\left( {3\sqrt{\frac{E_{0}}{5N_{0}}}} \right)}} \right)}},{{{BER}\left( i_{2} \right)} = {Q\left( \sqrt{\frac{E_{0}}{5N_{0}}} \right)}}}{{{where}\quad{Q(x)}} = {\frac{1}{\sigma\sqrt{2\pi}}{\int_{x}^{\infty}{{\mathbb{e}}^{- \frac{y^{2}}{2\sigma^{2}}}\quad{\mathbb{d}t}}}}}} & (29)\end{matrix}$

The BER performance that is obtained by means of the computer simulationof the present invention and the BER performance that is calculated bymeans of Equation (29) are a reasonable match. Further, as is evidentfrom the plots of FIGS. 15 and 16, if ICI does not exist, the BER of thereceiver of the present invention is no different from the BER obtainedby means of Equation (29) of a conventional matched filter basereceiver. Further, when ICI exists (when α₁=α₂=0.25), a conventionaldevice that executes nonlinear processing exhibits an inferiorequivalence performance to that of the receiver of the present inventionbased on the simulation results (shown as STD Alpha 0.25) and thesimulation results reveal that this inferiority is particularly markedin the event of a high Eb/N₀.

In recent years, a great number of methods have come to be developed toreduce sensitivity to ICI. For the sake of a fair comparison, DFEs(Decision Feedback Equalizers) of equal complexity are chosen aspossible alternate methods and shown in FIGS. 15 and 16 for the purposeof referencing simulation results of methods based on DFE (written asDFE).

(J) Conclusion

The effects of ICI in two adjacent channels of a multicarriercommunication system that adopts the 16 QAM modulation method wereinvestigated above. The performance of the conventional receiverdeteriorates very quickly as the coupling between the adjacent channelsincreases. This increases the BER of a non-coding system or codingsystem.

A bit-wise receiver based on posterior probability estimation washandled synthetically by using a Karkov chain approximation. Thereceiver of the present invention is a receiver based on the estimatedposterior probability. This receiver is a turbo receiver in which thereceiver of each subchannel passes information to the receiver of theadjacent subchannel and sequentially refines the posterior probabilitythat is estimated using information derived from the receiver of theadjacent subchannel.

Therefore, the turbo receiver of the present invention can substantiallyimprove BER performance in comparison with a conventional matched filterreceiver. This is because the nonlinear signal processing usesinformation that is obtained on the adjacent channel to maximize theposterior probability. In addition, the present invention executes a DFEequalizer that is widely used in order to cancel ICI by means ofintelligent feedback. The largest BER improvement is produced in a highS/N ratio area where ICI governs Gaussian noise. According to thesimulation results, the turbo receiver of the present invention is ableto achieve a favorable performance over a substantially wide range ofICI coupling coefficients.

Although described for QPSK (16-value QAM) of multi-value QAM, thepresent invention is not limited to sixteen values.

(K) Appendix A

The following is introduced to Equation (11) in order to simplify eachof the elements:ln P ₁(11)−ln P ₁(10)=ln P ₁(i ₁=1)+ln P ₁(i ₂=1)−ln P ₁(i ₁=1)−ln P₁(i₂=0)=Δ ln P ₁(i ₂)ln P ₁(01)−ln P ₁(00)=ln P ₁(i ₁=0)+ln P ₁(i ₂=1)−ln P ₁(i ₁=0)−ln P ₁(i₂=0)=Δ ln P ₁(i ₂)ln P ₁(11)+ln P ₁(10)−ln P ₁(01)−ln P ₁(00)=ln P ₁(11)−ln P ₁(01)+ln P₁(10)−ln P ₁(00)=2ΔP₁(i ₁)ln P ₂(11)−ln P ₂(10)=ln P ₂(i ₁=1)+ln P ₂(i ₂=1)−ln P ₂(i ₁=1)−ln P ₂(i₂=0)=Δ ln P ₁(i₂)ln P ₂(01)−ln P ₂(00)=ln P ₂(i ₁=0)+ln P ₂(i ₂=1)−ln P ₂(i ₁=0)−ln P ₂(i₂=0)=Δ ln P ₂(i ₂)ln P ₂(11)+ln P ₂(10)−ln P ₂(01)−ln P ₂(00)=ln P ₂(11)−ln P ₂(01)+ln P₂(10)−ln P ₂(00)=2ΔP ₂(i ₁)ln P ₂(11)−ln P ₂(01)=ln P ₂(i ₁=1)+ln P ₂(i ₂=1)−ln P ₂(i ₁=0)−ln P ₂(i₂=1)=Δ ln P ₂(i ₁)ln P ₂(10)−ln P ₂(00)=ln P ₂(i ₁=1)+ln P ₂(i ₂=0)−ln P ₂(i ₁=0)−ln P ₂(i₂=0)=Δ ln P ₂(i ₁)

When the common terms are removed, the following equation is establishedfrom Equation (2):${\ln\quad{P\left( {S_{j}/{y(t)}} \right)}} = {{\frac{2}{N_{0}}{\int_{0}^{T}{{{y(t)} \cdot {S_{j}(t)}}\quad{\mathbb{d}t}}}} - {\frac{E_{j}}{N_{0}}\quad\left( {{j = 0},1,2,{\ldots\quad 15}} \right)}}$where E_(j) is the energy of signal S_(j), such that:E _(j)=∫₀ ^(T) S _(j)(t)² dt

If, in order to simplify the notation, y is introduced as follows:${y->{\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}\quad{\mathbb{d}t}}}}},$the result is: $\begin{matrix}{{\ln\quad{P\left( {S_{j}/{y(t)}} \right)}} = {{\ln\quad{P\left( S_{j} \right)}} = {{y \cdot {S_{j}(t)}} - \frac{E_{j}}{N_{0}}}}} & {A(0)}\end{matrix}$

In accordance with the new notation i₁=1, the second term in Equation(12) becomes:ln{P(S ₀)·P ₂(11)+P(S ₁)·P ₂(10)+P(S ₂)·P ₂(01)+P(S ₃)·P ₂(00)}=0.25{lnP(S ₀)+ln P(S ₁)+ln P(S ₂)+ln P(S ₃)+(ln P ₂(11)+ln P ₂(10)+ln P₂(01)+ln P ₂(00))}+0.5(ln cosh{0.5(ln P(S ₀)−ln P(S ₁)+Δ ln P ₂(i₂))}+ln cosh{0.5(ln P(S ₂)−ln P(S ₃)+Δ ln P ₂(i ₂))})+ln cosh{0.25(lnP(S ₀))+ln P(S ₁)−ln P(S ₂)−ln P(S ₃)+2Δ ln P ₂(i ₁))}

The following equation is obtained from Equation A(0) and Table 2:ln P(S ₀)+ln P(S ₁)+ln P(S ₂)+ln P(S ₃)=−12·d·y−(36+20α²)·d ² /N ₀ln P(S ₀)−ln P(S ₁)=−2α·d·y−(12α+8α²)·d ² /N ₀ln P(S ₂)−ln P(S ₃)=−2α·d·y−(12α−8α²)·d ² /N ₀ln P(S ₀)+ln P(S ₁)−ln P(S ₂)−ln P(S ₃)=−8α·d·y−48α·d ² /N ₀and, finally, the following equation is obtained: $\begin{matrix}{{\ln\left\{ {{{P\left( S_{0} \right)} \cdot {P_{2}(11)}} + {{P\left( S_{1} \right)} \cdot {P_{2}(10)}} + {{P\left( S_{2} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{3} \right)} \cdot {P_{2}(00)}}} \right\}} = {0.25\left\{ {{{- 12} \cdot d \cdot y} - {\left( {36 + {20\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + \left( {{\ln\quad{P_{2}(11)}} + {\ln\quad{P_{2}(10)}} + {\ln\quad{P_{2}(01)}} + {\ln\quad{P_{2}(00)}}} \right\} + {0.5\left( {{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}\alpha}{\cdot d}{{\cdot y} - {\left( {{12\alpha} + {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {{\Delta ln}\quad{P\left( i_{2} \right)}}}} \right)} \right\}} + {\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\left( {{12\alpha} - {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {{\Delta ln}\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}} \right)} + {\ln\quad\cosh\left\{ {0.25\left( {{{- 8}{\alpha \cdot d \cdot y}} - {48{\alpha \cdot d^{2}}} + {2{\Delta ln}\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}} \right.}} & {A(1)}\end{matrix}$

Likewise, as a result of the new notation i₁=1, the third item ofEquation (12) becomes:ln{P(S ₄)·P ₂(11)+P(S ₅)·P ₂(10)+P(S ₆) P ₂(01)+P(S ₇)·P ₂(00)}=0.25{lnP(S ₄)+ln P(S ₅)+ln P(S ₆)+ln P(S ₇)+(ln P ₂(11)+ln P ₂(10)+ln P₂(01)+ln P ₂(00))}+0.5(ln cosh{0.5(ln P(S ₄)−ln P(S ₅)+Δ ln P ₂(i₂))}+ln cosh{0.5(ln P(S ₆)−ln P(S ₇)+Δ ln₂ P(i ₂))})+ln cosh{0.25(ln P(S₄)+ln P(S ₅)−ln P(S ₆)−ln P(S ₇)+2Δ ln P ₂(i ₁))}

The following equation is obtained from Equation A(0) and Table 2.ln P(S ₄)+ln P(S ₅)+ln P(S ₆)+ln P(S ₇)=−4·d·y−(4+20α)·d² /N ₀ln P(S ₄)−ln P(S ₅)=−2α·d·y−(4α+8α²)·d ² /N ₀ln P(S ₆)−ln P(S ₇)=−2α·d·y−(4α−8α²)·d ² /N ₀ln P(S ₄)+ln P(S ₆)−ln P(S ₇)−ln P(S ₈)=−8α·d·y−16α·d ²/N₀

Finally, the following equation is obtained: $\begin{matrix}{{\ln\left\{ {{{P\left( S_{4} \right)} \cdot {P_{2}(11)}} + {P{\left( S_{5} \right) \cdot P_{2}}(10)} + {{P\left( S_{6} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{7} \right)} \cdot {P_{2}(00)}}} \right\}} = {{0.25\left\{ {{{- 4} \cdot d \cdot y} - {\left( {4 + {20\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + \left( {{\ln\quad{P(11)}} + {\ln\quad{P(10)}} + {\ln\quad{P_{2}(01)}} + {\ln\quad{P_{2}(00)}}} \right)} \right\}} + {0.5\begin{pmatrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\left( {{4\alpha} + {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} - {\left( {{4\alpha} - {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix}} + {\ln\quad\cosh\left\{ {0.25\left( {{{- 8}{\alpha \cdot d \cdot y}} - {16{\alpha \cdot {d^{2}/N_{0}}}} + {2\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}}} & {A\quad(2)}\end{matrix}$

Similarly, in accordance with the new notation i₂=0, the fourth term ofEquation(12) becomes:ln{P(S ₈)·P ₂(11)+P(S ₉)·P ₂(10)+P(S ₁₀)·P ₂(01)+P(S ₁₁)·P₂(00)}=0.25{ln P(S ₈)+ln P(S ₉)+ln P(S ₁₀)+ln P(S ₁₁)+(ln P ₂(11)+ln P₂(10)+ln P ₂(01)+ln P ₂(00))}+0.5(ln cosh{0.5(ln P(S ₈)−ln P(S ₉)+Δ ln P₂(i ₂))}+ln cosh{0.5(ln P(S ₁₀)−ln P(S ₁₁)+Δ ln P ₂(i ₂))})+lncosh{0.25(ln P(S ₈)+ln P(S ₉)−ln P(S ₁₀)−ln P(S ₁₁)+2Δ ln P ₂(i ₁))}

The following equation is obtained from Equation A(0) and Table 2.ln P(S ₈)+ln P(S ₉)+ln P(S ₁₀)+ln P(S ₁₁)=−12·d·y−(36+20α)·d ² /N ₀ln P(S ₈)−ln P(S ₉)=−2α·d·y+(12α−8α²)·d ² /N ₀ln P(S ₁₀)−ln P(S ₁₁)=−2α·d·y+(12α+8α²)·d ² /N ₀ln P(S ₈)+ln P(S ₉)−ln P(S ₁₀)−ln P(S ₁₁)=−8α·d·y+48α·d ² /N ₀

Finally, the following equation is obtained: $\begin{matrix}{{\ln\left\{ {{{P\left( S_{8} \right)} \cdot {P_{2}(11)}} + {P{\left( S_{9} \right) \cdot P_{2}}(10)} + {{P\left( S_{10} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{11} \right)} \cdot {P_{2}(00)}}} \right\}} = {{0.25\left\{ {{{- 12} \cdot d \cdot y} - {\left( {36 + {20\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + \left( {{\ln\quad{P(11)}} + {\ln\quad{P(10)}} + {\ln\quad{P_{2}(01)}} + {\ln\quad{P_{2}(00)}}} \right)} \right\}} + {0.5\begin{pmatrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\left( {{12\alpha} - {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\left( {{12\alpha} + {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix}} + {\ln\quad\cosh\left\{ {0.25\left( {{{- 8}{\alpha \cdot d \cdot y}} + {48{\alpha \cdot d^{2}}} + {2\Delta\quad\ln\quad{P_{2}\left( i_{1} \right)}}} \right)} \right\}}}} & {A\quad(3)}\end{matrix}$

Likewise, in accordance with the new notation i₂=0, the fifth term inEquation (12) becomes:ln{P(S ₁₂)·P ₂(11)+P(S ₁₃)·P ₂(10)+P(S ₁₄)·P ₂(01)+P(S ₁₅)·P₂(00)}=0.25{ln P(S ₁₂)+ln P(S ₁₃)+ln P(S ₁₄)+ln P(S ₁₅)+(ln P ₂(11)+ln P₂(10)+ln P ₂(01)+ln P ₂(00))}+0.5(ln cosh{0.5(ln P(S ₁₂)−ln P(S ₁₃)+Δ lnP ₂(i ₂))}+ln cosh{0.5(ln P ₂(S ₁₄)−ln P(S ₁₅)+Δ ln P ₂(i ₂))})+lncosh{0.25(ln P(S ₁₂)+ln P(S ₁₃)−ln P(S ₁₄)−ln P(S ₁₄)+2Δ ln P ₂(i ₁))}

The following equation is obtained from Equation A(0) and Table 2:ln P(S ₁₂)+ln P(S ₁₃)+ln P(S ₁₄)+ln P(S ₁₅)=4·d·y−(4+20α)·d ²/N₀ln P(S₁₂)−ln P(S ₁₃)=−2α·d·y+(4α−8α²)−d ² /N ₀ln P(S ₁₄)−ln P(S ₁₅)=−2α·d·y+(4α+8α²)·d ² /N ₀ln P(S ₁₂)+ln P(S ₁₃)−ln P(S ₁₄)−ln P(S ₁₅)=2·y(t)/N ₀·(−8α·d)+16α·d ²/N ₀

Finally, the following equation is obtained: $\begin{matrix}{{\ln\left\{ {{{P\left( S_{12} \right)} \cdot {P_{2}(11)}} + {P{\left( S_{13} \right) \cdot P_{2}}(10)} + {{P\left( S_{14} \right)} \cdot {P_{2}(01)}} + {{P\left( S_{15} \right)} \cdot {P_{2}(00)}}} \right\}} = {{0.25\left\{ {{4 \cdot d \cdot y} - {\left( {4 + {20\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + \left( {{\ln\quad{P(11)}} + {\ln\quad{P(10)}} + {\ln\quad{P_{2}(01)}\ln\quad{P_{2}(00)}}} \right)} \right\}} + {0.5\begin{pmatrix}{{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\left( {{4\alpha} - {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}} +} \\{\ln\quad\cosh\left\{ {0.5\left( {{{- 2}{\alpha \cdot d \cdot y}} + {\left( {{4\alpha} + {8\alpha^{2}}} \right) \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{2}\left( i_{2} \right)}}} \right)} \right\}}\end{pmatrix}} + {\ln\quad\cosh\left\{ {0.25\left( {{{- 8}{\alpha \cdot d \cdot y}} + {16{\alpha \cdot d^{2}}} + {2\Delta\quad\ln\quad{P\left( i_{1} \right)}}} \right)} \right\}}}} & {A\quad(4)}\end{matrix}$

In order to simplify excessive complexity and calculations, thefollowing higher-order nonlinear elements in Equations (10) and (11)$\begin{matrix}{{\ln\quad\cosh\left\{ {0.5 \cdot \begin{pmatrix}{{\ln\quad{P_{1}(11)}} - {\ln\quad{P_{1}(10)}} +} \\{\ln\left( {{{P\left( S_{0} \right)}{P_{2}(11)}} + {{P\left( S_{1} \right)}{P_{2}(10)}} +} \right.} \\{\left. {{P\left( S_{2} \right){P_{2}(01)}} + {{P\left( S_{3} \right)}{P_{2}(00)}}} \right) -} \\{\ln\left( {{{P\left( S_{4} \right)}{P_{2}(11)}} + {{P\left( S_{5} \right)}{P_{2}(10)}} +} \right.} \\\left. {{P\left( S_{6} \right){P_{2}(01)}} + {{P\left( S_{7} \right)}{P_{2}(00)}}} \right)\end{pmatrix}} \right\}}{and}} & {A\quad(5)} \\{\ln\quad\cosh\left\{ {0.5 \cdot \begin{pmatrix}{{\ln\quad{P_{1}(01)}} - {\ln\quad{P_{1}(00)}} +} \\{\ln\left( {{{P\left( S_{8} \right)}{P_{2}(11)}} + {{P\left( S_{9} \right)}{P_{2}(10)}} +} \right.} \\{\left. {{P\left( S_{10} \right){P_{2}(01)}} + {{P\left( S_{11} \right)}{P_{2}(00)}}} \right) -} \\{\ln\left( {{{P\left( S_{12} \right)}{P_{2}(11)}} + {{P\left( S_{13} \right)}{P_{2}(10)}} +} \right.} \\\left. {{P\left( S_{14} \right){P_{2}(01)}} + {{P\left( S_{15} \right)}{P_{2}(00)}}} \right)\end{pmatrix}} \right\}} & {A\quad(6)}\end{matrix}$were not considered. In order to compensate for this, scaling(weighting) 0.25 was added to both nonlinear elements. The simulationresults show that this operation did not cause SNR deterioration(deterioration of 0.5 dB or more) for BER. Finally, Equations A(5) andA(6) are approximated by means of each of the following equations.$\begin{matrix}{{\ln\quad\cosh\left\{ {0.5 \cdot \begin{pmatrix}{{\ln\quad{P_{1}(11)}} - {\ln\quad{P_{1}(10)}} +} \\{\ln\left( {{{P\left( S_{0} \right)}{P_{2}(11)}} + {{P\left( S_{1} \right)}{P_{2}(10)}} +} \right.} \\{\left. {{P\left( S_{2} \right){P_{2}(01)}} + {{P\left( S_{3} \right)}{P_{2}(00)}}} \right) -} \\{\ln\left( {{{P\left( S_{4} \right)}{P_{2}(11)}} + {{P\left( S_{5} \right)}{P_{2}(10)}} +} \right.} \\\left. {{P\left( S_{6} \right){P_{2}(01)}} + {{P\left( S_{7} \right)}{P_{2}(00)}}} \right)\end{pmatrix}} \right\}} \approx {{0.25 \cdot \ln}\quad\cosh\left\{ {0.5\left( {{{- 2} \cdot \alpha \cdot d \cdot y} - {8 \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}}} \right)} \right\}}} & {A(7)} \\{{\ln\quad\cosh\left\{ {0.5 \cdot \begin{pmatrix}{{\ln\quad{P_{1}(11)}} - {\ln\quad{P_{1}(10)}} +} \\{\ln\left( {{{P\left( S_{0} \right)}{P(11)}} + {{P\left( S_{1} \right)}{P(10)}} +} \right.} \\{\left. {{P\left( S_{2} \right){P(01)}} + {{P\left( S_{3} \right)}{P(00)}}} \right) -} \\{\ln\left( {{{P\left( S_{4} \right)}{P(11)}} + {{P\left( S_{5} \right)}{P(10)}} +} \right.} \\\left. {{P\left( S_{6} \right){P(01)}} + {{P\left( S_{7} \right)}{P(00)}}} \right)\end{pmatrix}} \right\}} \approx {{0.25 \cdot \ln}\quad\cosh\left\{ {0.5\left( {{{- 2} \cdot \alpha \cdot d \cdot y} + {8 \cdot {d^{2}/N_{0}}} + {\Delta\quad\ln\quad{P_{1}\left( i_{2} \right)}}} \right)} \right\}}} & {A(8)}\end{matrix}$

As many apparently widely different embodiments of the present inventioncan be made without departing from the spirit and scope thereof, it isto be understood that the invention is not limited to the specificembodiments thereof except as defined in the appended claims.

1. A communication system that sends and receives signals via twoadjacent channels in which interchannel interference exists, comprising:a transmitter device that transmits data of one unit in a plurality ofbits via each channel; a receiver device provided in each channel thatgenerates a soft decision target value for each of a plurality ofreceived bits inputted from the corresponding channel and makes a softdecision with respect to the plurality of received bits by using therespective soft decision target values; and means for inputting the softdecision target values of the plurality of received bits of the receiverdevice of one channel to the receiver device of the other channel,wherein the receiver device adjusts the respective soft decision targetvalues of its own channel by using the respective soft decision targetvalues of the plurality of bits inputted from the receiver device of theother channel and makes a decision with respect to the received bits onthe basis of the soft decision target values.
 2. The communicationsystem according to claim 1, wherein the receiver device comprises: asoft decision target value generation unit provided in correspondencewith each of the plurality of received bits that generates soft decisiontarget values that correspond with each of the received bits; and a softdecision unit that makes a soft decision with respect to the pluralityof received bits by using the respective soft decision target values,wherein the soft decision target value generation unit adjusts its ownsoft decision target values by using soft decision target values thatare inputted from the receiver device of the other channel.
 3. Thecommunication system according to claim 1, wherein the receiver devicecomprises: a soft decision target value generation unit provided incorrespondence with each of the plurality of received bits thatgenerates soft decision target values that correspond with each of thereceived bits; and a soft decision unit that makes a soft decision withrespect to the plurality of received bits by using the respective softdecision target values, wherein the soft decision target valuegeneration unit comprises: means for adjusting the soft decision targetvalue of bits of interest by using soft decision target values that areinputted from the receiver device of the other channel; and means foradjusting the soft decision target values of the bits of interest byusing soft decision target values of the other bits excluding the bitsof interest.
 4. The communication system according to claim 1, whereinthe data of one unit is constituted by a plurality of bits constitutingan in-phase component that has been obtained by multi-value QAMmodulation.
 5. The communication system according to claim 1, whereinthe data of one unit is constituted by a plurality of bits constitutinga quadrature component that has been obtained by multi-value QAMmodulation.
 6. The communication system according to claim 1, wherein,in a case where the data of one unit is two-bit data of an in-phasecomponent or quadrature component that has been obtained by multi-valueQAM modulation, the receiver portion of the first bit of the channel ofinterest of the receiver device comprises: two first and secondcorrelation means that integrate the multiplication result obtained bymultiplying an input signal by predetermined reference signals; threefirst to third nonlinear units having a transmission function of anamplitude limiter comprising a linear region; a multiplication unit thatmultiplies the outputs of the nonlinear units by weighting functions; asynthesizer that generates the soft decision target value of the firstbit of the channel of interest by synthesizing each weightedmultiplication unit output and the output of the first correlationmeans; an adder circuit that adds the soft decision target values of thefirst and second bits of the other channel to the output signals fromthe first and second correlation means respectively and then inputs theaddition results to the first and second nonlinear units respectively;and an adder circuit that adds the soft decision target value of thesecond bit of the channel of interest to the output signal from thesecond correlation means and inputs the addition result to the thirdnonlinear unit.
 7. The communication system according to claim 1,wherein, in a case where the data of one unit is two-bit data of anin-phase component or quadrature component that has been obtained bymulti-value QAM modulation, the receiver portion of the second bit ofthe channel of interest of the receiver device comprises: three first,second and third-correlation means that integrate multiplication resultsobtained by multiplying an input signal by predetermined referencesignals; three first to third nonlinear units having a transmissionfunction of an amplitude limiter comprising a linear region; an addercircuit that adds the soft decision target values of the second andfirst bits of the other channel to the output signals from the secondand third correlation means respectively and then inputs the additionresults to the first and second nonlinear units respectively; acalculation unit that multiplies the output signal from the firstcorrelation means by a predetermined value and then adds themultiplication result to the outputs of the first and second nonlinearunits; and an adder circuit that adds the soft decision target value ofthe first bit of the channel of interest to the output of thecalculation unit and then inputs the addition result to the thirdnonlinear unit, wherein the soft decision target value of the second bitof the channel of interest is produced on the basis of the output of thethird nonlinear unit.
 8. A receiver device of a channel of interest in acommunication system that sends and receives data of one unit in aplurality of bits via each of two adjacent channels in whichinterchannel interference exists, comprising: means for generating softdecision target values for each of the plurality of received bitsinputted from the channel of interest; and a soft decision unit thatmakes a soft decision with respect to the plurality of received bits byusing the respective soft decision target values, wherein the softdecision target value generating means adjust their own soft decisiontarget values by using the respective soft decision target values of theplurality of bits inputted from the receiver device of the other channeland the soft decision unit makes a decision with respect to the receivedbits on the basis of the soft decision target values.
 9. The receiverdevice according to claim 8, wherein the soft decision target valuegenerating means comprise: a soft decision target value generation unitcorresponding with each of a plurality of received bits that generatessoft decision target values that correspond with the received bits. 10.A receiver device of a channel of interest in a communication systemthat sends and receives data of one unit in a plurality of bits via eachof two adjacent channels in which interchannel interference exists,comprising: a soft decision target value generation unit provided incorrespondence with each of the plurality of received bits thatgenerates soft decision target values that correspond with each of thereceived bits; and a soft decision unit that makes a soft decision withrespect to the plurality of received bits by using the respective softdecision target values, wherein the soft decision target valuegeneration unit comprises: means for adjusting the soft decision targetvalue of bits of interest by using soft decision target values that areinputted from the receiver device of the other channel; and means foradjusting the soft decision target values of the bits of interest byusing soft decision target values of the other bits excluding the bitsof interest.
 11. The receiver device according to claim 8, wherein thedata of one unit is constituted by a plurality of bits constituting anin-phase component that has been obtained by multi-value QAM modulation.12. The receiver device according to claim 8, wherein the data of oneunit is constituted by a plurality of bits constituting a quadraturecomponent that has been obtained by multi-value QAM modulation.
 13. Thereceiver device according to claim 9, wherein, in a case where the dataof one unit is two-bit data of an in-phase component or quadraturecomponent that has been obtained by multi-value QAM modulation, the softdecision target value generation unit of the first bit comprises: twofirst and second correlation means that integrate the multiplicationresults obtained by multiplying an input signal by predeterminedreference signals; three first to third nonlinear units having atransmission function of an amplitude limiter comprising a linearregion; a multiplication unit that multiplies the outputs of thenonlinear units by weighting functions; a synthesizer that generates thesoft decision target value of the first bit of the channel of interestby synthesizing each weighted multiplication unit output and the outputof the first correlation means; an adder circuit that adds the softdecision target values of the first and second bits of the other channelto the output signals from the first and second correlation meansrespectively and then inputs the addition results to the first andsecond nonlinear units respectively; and an adder circuit that adds thesoft decision target value of the second bit of the channel of interestto the output signal from the second correlation means and inputs theaddition result to the third nonlinear unit.
 14. The receiver deviceaccording to claim 9, wherein, in a case where the data of one unit istwo-bit data of an in-phase component or quadrature component that hasbeen obtained by multi-value QAM modulation, the soft decision targetvalue generation unit of the second bit comprises: three first, secondand third correlation means that integrate the multiplication resultsobtained by multiplying an input signal by predetermined referencesignals; three first to third nonlinear units having a transmissionfunction of an amplitude limiter comprising a linear region; an addercircuit that adds the soft decision target values of the second andfirst bits of the other channel to the output signals from the secondand third correlation means respectively and then inputs the additionresults to the first and second nonlinear units respectively; acalculation unit that multiplies the output signal from the firstcorrelation means by a predetermined value and then adds themultiplication result to the outputs of the first and second nonlinearunits; and an adder circuit that adds the soft decision target value ofthe first bit of the channel of interest to the output of thecalculation unit and then inputs the addition result to the thirdnonlinear unit, wherein the soft decision target value of the second bitof the channel of interest is produced on the basis of the output of thethird nonlinear unit.